PUBLISHED PAPERS:

[149] B. Brešar, C. Bujtás, P. Dokyeesun, and T. Dravec, “Thresholds for the biased Maker-Breaker domination games,” Discrete Math. Theor. Comput. Sci., vol. 27, no. 3, p. Paper No. 19, 19, 2025.

[148]  B. Brešar, S. Klavžar, and B. Samadi, “Total k-coalition: bounds, exact values and an application to double coalition,” Discrete Math. Theor. Comput. Sci., vol. 27, no. 3, p. Paper No. 3, 18, 2025.

[147] B. Brešar, T. Dravec, M. G. Cornet, and M. A. Henning, “k-domination invariants on Kneser graphs,” Ars Math. Contemp., vol. 25, no. 4, p. Paper No. 2, 16, 2025.

[146] B. Brešar, S. Klavžar, B. Samadi, and I. G. Yero, “Injective colorings of Sierpiński-like graphs and Kneser graphs,” Graphs Combin., vol. 41, no. 4, p. Paper No. 83, 22, 2025, doi: 10.1007/s00373-025-02952-3.

[145] B. Brešar, K. Kuenzel, and D. F. Rall, “Claw-free cubic graphs are (1,1,2,2)-colorable,” Discrete Math., vol. 348, no. 8, p. Paper No. 114477, 9, 2025, doi: 10.1016/j.disc.2025.114477.

[144] B. Brešar, T. Dravec, J. Hedžet, and B. Samadi, “Induced matching vs edge open packing: trees and product graphs,” Discrete Math., vol. 348, no. 7, p. Paper No. 114458, 19, 2025, doi: 10.1016/j.disc.2025.114458.

[143] B. Brešar, J. Ferme, P. Holub, M. Jakovac, and P. Melicharová, “S-packing colorings of distance graphs with distance sets of cardinality 2,” Appl. Math. Comput., vol. 490, p. Paper No. 129200, 13, 2025, doi: 10.1016/j.amc.2024.129200.

[142] B. Brešar and J. Hedžet, “Bootstrap percolation in strong products of graphs,” Electron. J. Combin., vol. 31, no. 4, p. Paper No. 4.35, 22, 2024, doi: 10.37236/11826.

[141] B. Brešar and B. Samadi, “Edge open packing: complexity, algorithmic aspects, and bounds,” Theoret. Comput. Sci., vol. 1022, p. Paper No. 114884, 10, 2024, doi: 10.1016/j.tcs.2024.114884.

[140] B. Brešar, M. Gracia Cornet, T. Dravec, and M. Henning, “Bounds on zero forcing using (upper) total domination and minimum degree,” Bull. Malays. Math. Sci. Soc., vol. 47, no. 5, p. Paper No. 143, 18, 2024, doi: 10.1007/s40840-024-01744-x.

[139] B. Brešar and M. A. Henning, “Best possible upper bounds on the restrained domination number of cubic graphs,” J. Graph Theory, vol. 106, no. 4, pp. 763–815, 2024, doi: 10.1002/jgt.23095.

[138] B. Brešar, C. Bujtás, V. Iršič, D. F. Rall, and Z. Tuza, “Indicated domination game,” Discrete Math., vol. 347, no. 9, p. Paper No. 114060, 10, 2024, doi: 10.1016/j.disc.2024.114060.

[137] B. Brešar, T. Dravec, A. Erey, and J. Hedžet, “Spreading in graphs,” Discrete Appl. Math., vol. 353, pp. 139–150, 2024, doi: 10.1016/j.dam.2024.04.019.

[136] B. Brešar, S. Klavžar, and D. F. Rall, “Packings in bipartite prisms and hypercubes,” Discrete Math., vol. 347, no. 4, p. Paper No. 113875, 6, 2024, doi: 10.1016/j.disc.2024.113875.

[135] B. Brešar and I. G. Yero, “Lower (total) mutual-visibility number in graphs,” Appl. Math. Comput., vol. 465, p. Paper No. 128411, 11, 2024, doi: 10.1016/j.amc.2023.128411.

[134] B. Brešar, A. Pandey, and G. Sharma, “Computation of Grundy dominating sequences in (co-)bipartite graphs,” Comput. Appl. Math., vol. 42, no. 8, p. Paper No. 359, 17, 2023, doi: 10.1007/s40314-023-02500-w.

[133] P. Manuel, B. Brešar, and S. Klavžar, “Geodesic packing in graphs,” Appl. Math. Comput., vol. 459, p. Paper No. 128277, 7, 2023, doi: 10.1016/j.amc.2023.128277.

[132] S. Akbari, A. Beikmohammadi, Boštjan Brešar, T. Dravec, M. M. Habibollahi, and N. Movarraei, “On the chromatic edge stability index of graphs,” European J. Combin., vol. 111, p. Paper No. 103690, 16, 2023, doi: 10.1016/j.ejc.2023.103690.

[131] G. Bacsó, B. Brešar, K. Kuenzel, and D. F. Rall, “Graphs with equal Grundy domination and independence number,” Discrete Optim., vol. 48, p. Paper No. 100777, 15, 2023, doi: 10.1016/j.disopt.2023.100777.

[130] B. Brešar, T. Dravec, and E. Kleszcz, “Uniquely colorable graphs up to automorphisms,” Appl. Math. Comput., vol. 450, p. Paper No. 128007, 10, 2023, doi: 10.1016/j.amc.2023.128007.

[129] B. Brešar, B. Samadi, and I. G. Yero, “Injective coloring of graphs revisited,” Discrete Math., vol. 346, no. 5, p. Paper No. 113348, 12, 2023, doi: 10.1016/j.disc.2023.113348.

[128] P. Manuel, B. Brešar, and S. Klavžar, “The geodesic transversal problem on some networks,” Comput. Appl. Math., vol. 42, no. 1, p. Paper No. 59, 12, 2023, doi: 10.1007/s40314-023-02199-9.

[127] S. Anderson, B. Brešar, S. Klavžar, K. Kuenzel, and D. F. Rall, “Orientable domination in product-like graphs,” Discrete Appl. Math., vol. 326, pp. 62–69, 2023, doi: 10.1016/j.dam.2022.11.003.

[126] B. Brešar, A. Pandey, and G. Sharma, “Computational aspects of some vertex sequences of Grundy domination-type,” Indian J. Discrete Math., vol. 8, no. 1, pp. 21–38, 2022.

[125] B. Brešar and D. Mesarič Štesl, “The competition-independence game with prevention,” Filomat, vol. 36, no. 18, pp. 6197–6213, 2022.

[124] B. Brešar and D. Štesl, “The independence coloring game on graphs,” Quaest. Math., vol. 45, no. 9, pp. 1413–1434, 2022, doi: 10.2989/16073606.2021.1947919.

[123] B. Brešar, K. Kuenzel, and D. F. Rall, “Domination in digraphs and their direct and Cartesian products,” J. Graph Theory, vol. 99, no. 3, pp. 359–377, 2022, doi: 10.1002/jgt.22744.

[122] B. Brešar, T. Dravec, A. Gorzkowska, and E. Kleszcz, “Graphs with a unique maximum independent set up to automorphisms,” Discrete Appl. Math., vol. 317, pp. 124–135, 2022, doi: 10.1016/j.dam.2022.04.003.

[121] B. Brešar and J. Ferme, “Graphs that are critical for the packing chromatic number,” Discuss. Math. Graph Theory, vol. 42, no. 2, pp. 569–589, 2022, doi: 10.7151/dmgt.2298.

[120] P. Manuel, B. Brešar, and S. Klavžar, “The geodesic-transversal problem,” Appl. Math. Comput., vol. 413, p. Paper No. 126621, 11, 2022, doi: 10.1016/j.amc.2021.126621.

[119] B. Brešar and S. Brezovnik, “Grundy domination and zero forcing in regular graphs,” Bull. Malays. Math. Sci. Soc., vol. 44, no. 6, pp. 3637–3661, 2021, doi: 10.1007/s40840-021-01134-7.

[118] B. Brešar, J. Ferme, and K. Kamenická, “S-packing colorings of distance graphs G(\BbbZ, {2,t} ),” Discrete Appl. Math., vol. 298, pp. 143–154, 2021, doi: 10.1016/j.dam.2021.04.001.

[117] B. Brešar, N. Gastineau, T. Gologranc, and O. Togni, “On a vertex-edge marking game on graphs,” Ann. Comb., vol. 25, no. 1, pp. 179–194, 2021, doi: 10.1007/s00026-021-00524-9.

[116] B. Brešar, B. L. Hartnell, M. A. Henning, K. Kuenzel, and D. F. Rall, “A new framework to approach Vizing’s conjecture,” Discuss. Math. Graph Theory, vol. 41, no. 3, pp. 749–762, 2021, doi: 10.7151/dmgt.2293.

[115] B. Brešar, M. Jakovac, and D. Štesl, “Indicated coloring game on Cartesian products of graphs,” Discrete Appl. Math., vol. 289, pp. 320–326, 2021, doi: 10.1016/j.dam.2020.11.007.

[114] B. Brešar, Cs. Bujtás, T. Gologranc, S. Klavžar, G. Košmrlj, T. Marc, B. Patkós, Zs. Tuza, and M. Vizer, “On Grundy total domination number in product graphs,” Discuss. Math. Graph Theory, vol. 41, no. 1, pp. 225–247, 2021, doi: 10.7151/dmgt.2184.

[113] B. Brešar, T. Gologranc, M. A. Henning, and T. Kos, “On the L-Grundy domination number of a graph,” Filomat, vol. 34, no. 10, pp. 3205–3215, 2020.

[112] B. Brešar, “Rainbow domination in graphs,” in Topics in domination in graphs, vol. 64, Springer, Cham, [2020] ©2020, pp. 411–443. doi: 10.1007/978-3-030-51117-3\_12.

[111] B. Brešar, N. Gastineau, and O. Togni, “Packing colorings of subcubic outerplanar graphs,” Aequationes Math., vol. 94, no. 5, pp. 945–967, 2020, doi: 10.1007/s00010-020-00721-6.

[110] B. Brešar, J. Ferme, S. Klavžar, and D. F. Rall, “A survey on packing colorings,” Discuss. Math. Graph Theory, vol. 40, no. 4, pp. 923–970, 2020, doi: 10.7151/dmgt.2320.

[109] B. Brešar and M. A. Henning, “A 3/4-approximation of Vizing’s conjecture for claw-free graphs,” Discrete Appl. Math., vol. 284, pp. 416–422, 2020, doi: 10.1016/j.dam.2020.03.056.

[108] B. Brešar and M. Valencia-Pabon, “On the P₃-hull number of Hamming graphs,” Discrete Appl. Math., vol. 282, pp. 48–52, 2020, doi: 10.1016/j.dam.2019.11.011.

[107] B. Brešar, S. Klavžar, and N. Movarraei, “Critical graphs for the chromatic edge-stability number,” Discrete Math., vol. 343, no. 6, pp. 111845, 7, 2020, doi: 10.1016/j.disc.2020.111845.

[106] B. Brešar, K. Kuenzel, and D. F. Rall, “Graphs with a unique maximum open packing,” Indian J. Discrete Math., vol. 5, no. 1, pp. 37–55, 2019.

[105] B. Brešar, N. Gastineau, S. Klavžar, and O. Togni, “Exact distance graphs of product graphs,” Graphs Combin., vol. 35, no. 6, pp. 1555–1569, 2019, doi: 10.1007/s00373-019-02089-0.

[104] B. Brešar, T. Kos, and P. D. Torres, “Grundy domination and zero forcing in Kneser graphs,” Ars Math. Contemp., vol. 17, no. 2, pp. 419–430, 2019, doi: 10.26493/1855-3974.1881.384.

[103] B. Brešar, Cs. Bujtás, T. Gologranc, S. Klavžar, G. Košmrlj, T. Marc, B. Patkós, Zs. Tuza, and M. Vizer, “The variety of domination games,” Aequationes Math., vol. 93, no. 6, pp. 1085–1109, 2019, doi: 10.1007/s00010-019-00661-w.

[102] B. Brešar, T. Kos, R. Krivoš-Belluš, and G. Semanišin, “Hitting subgraphs in P₄-tidy graphs,” Appl. Math. Comput., vol. 352, pp. 211–219, 2019, doi: 10.1016/j.amc.2019.01.074.

[101] B. Brešar and M. Valencia-Pabon, “Independence number of products of Kneser graphs,” Discrete Math., vol. 342, no. 4, pp. 1017–1027, 2019, doi: 10.1016/j.disc.2018.12.017.

[100] B. Brešar and J. Ferme, “Packing coloring of Sierpiński-type graphs,” Aequationes Math., vol. 92, no. 6, pp. 1091–1118, 2018, doi: 10.1007/s00010-018-0561-8.

[99] B. Brešar, T. R. Hartinger, T. Kos, and M. Milanič, “1-perfectly orientable K₄-minor-free and outerplanar graphs,” Discrete Appl. Math., vol. 248, pp. 33–45, 2018, doi: 10.1016/j.dam.2017.09.017.

[98] B. Brešar and N. Movarraei, “On the number of maximal independent sets in minimum colorings of split graphs,” Discrete Appl. Math., vol. 247, pp. 352–356, 2018, doi: 10.1016/j.dam.2018.03.083.

[97] B. Brešar, T. R. Hartinger, T. Kos, and M. Milanič, “On total domination in the Cartesian product of graphs,” Discuss. Math. Graph Theory, vol. 38, no. 4, pp. 963–976, 2018, doi: 10.7151/dmgt.2039.

[96] B. Brešar and J. Ferme, “An infinite family of subcubic graphs with unbounded packing chromatic number,” Discrete Math., vol. 341, no. 8, pp. 2337–2342, 2018, doi: 10.1016/j.disc.2018.05.004.

[95] B. Brešar, S. Klavžar, D. F. Rall, and K. Wash, “Packing chromatic number versus chromatic and clique number,” Aequationes Math., vol. 92, no. 3, pp. 497–513, 2018, doi: 10.1007/s00010-017-0520-9.

[94] B. Brešar, T. Kos, G. Nasini, and P. Torres, “Total dominating sequences in trees, split graphs, and under modular decomposition,” Discrete Optim., vol. 28, pp. 16–30, 2018, doi: 10.1016/j.disopt.2017.10.002.

[93] B. Brešar, T. Gologranc, and T. Kos, “Convex and isometric domination of (weak) dominating pair graphs,” Theoret. Comput. Sci., vol. 730, pp. 32–43, 2018, doi: 10.1016/j.tcs.2018.03.023.

[92] F. Bonomo, B. Brešar, L. N. Grippo, M. Milanič, and M. D. Safe, “Domination parameters with number 2: interrelations and algorithmic consequences,” Discrete Appl. Math., vol. 235, pp. 23–50, 2018, doi: 10.1016/j.dam.2017.08.017.

[91] B. Brešar, B. L. Hartnell, and D. F. Rall, “Uniformly dissociated graphs,” Ars Math. Contemp., vol. 13, no. 2, pp. 293–306, 2017, doi: 10.26493/1855-3974.1013.46a.

[90] B. Brešar, Cs. Bujtás, T. Gologranc, S. Klavžar, G. Košmrlj, B. Patkós, Zs. Tuza, and M. Vizer, “Grundy dominating sequences and zero forcing sets,” Discrete Optim., vol. 26, pp. 66–77, 2017, doi: 10.1016/j.disopt.2017.07.001.

[89] B. Brešar, “Improving the Clark-Suen bound on the domination number of the Cartesian product of graphs,” Discrete Math., vol. 340, no. 10, pp. 2398–2401, 2017, doi: 10.1016/j.disc.2017.05.007.

[88] B. Brešar and M. A. Henning, “The game total domination problem is log-complete in PSPACE,” Inform. Process. Lett., vol. 126, pp. 12–17, 2017, doi: 10.1016/j.ipl.2017.05.007.

[87] B. Brešar, P. Dorbec, S. Klavžar, and G. Košmrlj, “How long can one bluff in the domination game?,” Discuss. Math. Graph Theory, vol. 37, no. 2, pp. 337–352, 2017, doi: 10.7151/dmgt.1899.

[86] B. Brešar, S. Klavžar, D. F. Rall, and K. Wash, “Packing chromatic number under local changes in a graph,” Discrete Math., vol. 340, no. 5, pp. 1110–1115, 2017, doi: 10.1016/j.disc.2016.09.030.

[85] B. Brešar, S. Klavžar, D. F. Rall, and K. Wash, “Packing chromatic number, (1,1,2,2)-colorings, and characterizing the Petersen graph,” Aequationes Math., vol. 91, no. 1, pp. 169–184, 2017, doi: 10.1007/s00010-016-0461-8.

[84] B. Brešar, Cs. Bujtás, T. Gologranc, S. Klavžar, G. Košmrlj, B. Patkós, Zs. Tuza, and M. Vizer, “Dominating sequences in grid-like and toroidal graphs,” Electron. J. Combin., vol. 23, no. 4, p. Paper 4.34, 19, 2016, doi: 10.37236/6269.

[83] B. Brešar, T. Gologranc, and T. Kos, “Dominating sequences under atomic changes with applications in Sierpiński and interval graphs,” Appl. Anal. Discrete Math., vol. 10, no. 2, pp. 518–531, 2016, doi: 10.2298/AADM161005024B.

[82] B. Brešar, P. Dorbec, S. Klavžar, G. Košmrlj, and G. Renault, “Complexity of the game domination problem,” Theoret. Comput. Sci., vol. 648, pp. 1–7, 2016, doi: 10.1016/j.tcs.2016.07.025.

[81] B. Brešar, S. Klavžar, and D. F. Rall, “Packing chromatic number of base-3 Sierpiński graphs,” Graphs Combin., vol. 32, no. 4, pp. 1313–1327, 2016, doi: 10.1007/s00373-015-1647-x.

[80] B. Brešar, M. A. Henning, and D. F. Rall, “Total dominating sequences in graphs,” Discrete Math., vol. 339, no. 6, pp. 1665–1676, 2016, doi: 10.1016/j.disc.2016.01.017.

[79] B. Brešar, “Vizing’s conjecture for graphs with domination number 3—a new proof,” Electron. J. Combin., vol. 22, no. 3, p. Paper 3.38, 8, 2015, doi: 10.37236/5182.

[78] B. Brešar and D. F. Rall, “On Cartesian products having a minimum dominating set that is a box or a stairway,” Graphs Combin., vol. 31, no. 5, pp. 1263–1270, 2015, doi: 10.1007/s00373-014-1486-1.

[77] B. Brešar, M. Changat, T. Gologranc, and B. Sukumaran, “Cographs which are cover-incomparability graphs of posets,” Order, vol. 32, no. 2, pp. 179–187, 2015, doi: 10.1007/s11083-014-9324-x.

[76] B. Brešar, S. Klavžar, G. Košmrlj, and D. F. Rall, “Guarded subgraphs and the domination game,” Discrete Math. Theor. Comput. Sci., vol. 17, no. 1, pp. 161–168, 2015.

[75]  L. Alcón, B. Brešar, T. Gologranc, M. Gutierrez, T. Kraner Šumenjak, I. Peterin, and A. Tepeh, “Toll convexity,” European J. Combin., vol. 46, pp. 161–175, 2015, doi: 10.1016/j.ejc.2015.01.002.

[74]  B. Brešar, T. Gologranc, M. Milanič, D. F. Rall, and R. Rizzi, “Dominating sequences in graphs,” Discrete Math., vol. 336, pp. 22–36, 2014, doi: 10.1016/j.disc.2014.07.016.

[73] B. Brešar, R. Krivoš-Belluš, G. Semanišin, and P. Šparl, “On the weighted k-path vertex cover problem,” Discrete Appl. Math., vol. 177, pp. 14–18, 2014, doi: 10.1016/j.dam.2014.05.042.

[72] B. Brešar, M. Changat, T. Gologranc, M. Kovše, and B. Sukumaran, “Cover-incomparability graphs and 2-colored diagrams of posets,” Taiwanese J. Math., vol. 18, no. 4, pp. 1243–1255, 2014, doi: 10.11650/tjm.18.2014.3697.

[71] B. Brešar, P. Dorbec, S. Klavžar, and G. Košmrlj, “Domination game: effect of edge- and vertex-removal,” Discrete Math., vol. 330, pp. 1–10, 2014, doi: 10.1016/j.disc.2014.04.015.

[70] K. Balakrishnan, B. Brešar, M. Changat, S. Klavžar, A. Vesel, and P.  Žigert Pleteršek, “Equal opportunity networks, distance-balanced graphs, and Wiener game,” Discrete Optim., vol. 12, pp. 150–154, 2014, doi: 10.1016/j.disopt.2014.01.002.

[69] B. Brešar and T. K. Šumenjak, “The hypergraph of Θ-classes and Θ-graphs of partial cubes,” Ars Combin., vol. 113, pp. 225–239, 2014.

[68] B. Brešar, J. Chalopin, V. Chepoi, T. Gologranc, and D. Osajda, “Bucolic complexes,” Adv. Math., vol. 243, pp. 127–167, 2013, doi: 10.1016/j.aim.2013.04.009.

[67] B. Brešar, M. Jakovac, J. Katrenič, G. Semanišin, and A. Taranenko, “On the vertex k-path cover,” Discrete Appl. Math., vol. 161, no. 13–14, pp. 1943–1949, 2013, doi: 10.1016/j.dam.2013.02.024.

[66] B. Brešar, J. Chalopin, V. Chepoi, M. Kovše, A. Labourel, and Y. Vaxès, “Retracts of products of chordal graphs,” J. Graph Theory, vol. 73, no. 2, pp. 161–180, 2013, doi: 10.1002/jgt.21665.

[65] B. Brešar, S. Klavžar, G. Košmrlj, and D. F. Rall, “Domination game: extremal families of graphs for 3/5-conjectures,” Discrete Appl. Math., vol. 161, no. 10–11, pp. 1308–1316, 2013, doi: 10.1016/j.dam.2013.01.025.

[64] B. Brešar, S. Klavžar, and D. F. Rall, “Domination game played on trees and spanning subgraphs,” Discrete Math., vol. 313, no. 8, pp. 915–923, 2013, doi: 10.1016/j.disc.2013.01.014.

[63] K. Balakrishnan, B. Brešar, M. Changat, S. Klavžar, I. Peterin, and A. R. Subhamathi, “Almost self-centered median and chordal graphs,” Taiwanese J. Math., vol. 16, no. 5, pp. 1911–1922, 2012, doi: 10.11650/twjm/1500406804.

[62] D. Bokal, B. Brešar, and J. Jerebic, “A generalization of Hungarian method and Hall’s theorem with applications in wireless sensor networks,” Discrete Appl. Math., vol. 160, no. 4–5, pp. 460–470, 2012, doi: 10.1016/j.dam.2011.11.007.

[61] B. Brešar, P. Dorbec, W. Goddard, M.A. Henning, S. Klavžar, D.F. Rall, “Vizing’s conjecture: a survey and recent results,” J. Graph Theory, vol. 69, no. 1, pp. 46–76, 2012, doi: 10.1002/jgt.20565.

[60] B. Brešar and T. Gologranc, “On a local 3-Steiner convexity,” European J. Combin., vol. 32, no. 8, pp. 1222–1235, 2011, doi: 10.1016/j.ejc.2011.06.001.

[59] B. Brešar, T. K. Šumenjak, and A. Tepeh, “The geodetic number of the lexicographic product of graphs,” Discrete Math., vol. 311, no. 16, pp. 1693–1698, 2011, doi: 10.1016/j.disc.2011.04.004.

[58] B. Brešar, F. Kardoš, J. Katrenič, and G. Semanišin, “Minimum k-path vertex cover,” Discrete Appl. Math., vol. 159, no. 12, pp. 1189–1195, 2011, doi: 10.1016/j.dam.2011.04.008.

[57] B. Brešar, M. Kovše, and A. Tepeh, “Geodetic sets in graphs,” in Structural analysis of complex networks, Birkhäuser/Springer, New York, 2011, pp. 197–218. doi: 10.1007/978-0-8176-4789-6\_8.

[56] K. Balakrishnan, B. Brešar, M. Kovše, M. Changat, A. R. Subhamathi, and S. Klavžar, “Simultaneous embeddings of graphs as median and antimedian subgraphs,” Networks, vol. 56, no. 2, pp. 90–94, 2010, doi: 10.1002/net.20350.

[55] B. Brešar, S. Klavžar, and D. F. Rall, “Domination game and an imagination strategy,” SIAM J. Discrete Math., vol. 24, no. 3, pp. 979–991, 2010, doi: 10.1137/100786800.

[54] B. Brešar, M. Changat, T. Gologranc, J. Mathews, and A. Mathews, “Cover-incomparability graphs and chordal graphs,” Discrete Appl. Math., vol. 158, no. 16, pp. 1752–1759, 2010, doi: 10.1016/j.dam.2010.07.001.

[53] B. Brešar, M. Changat, A. R. Subhamathi, and A. Tepeh, “The periphery graph of a median graph,” Discuss. Math. Graph Theory, vol. 30, no. 1, pp. 17–32, 2010, doi: 10.7151/dmgt.1473.

[52] K. Balakrishnan, B. Brešar, M. Changat, S. Klavžar, M. Kovše, and A. R. Subhamathi, “Computing median and antimedian sets in median graphs,” Algorithmica, vol. 57, no. 2, pp. 207–216, 2010, doi: 10.1007/s00453-008-9200-4.

[51] B. Brešar and T. K. Šumenjak, “Θ-graphs of partial cubes and strong edge colorings,” Ars Combin., vol. 93, pp. 417–429, 2009.

[50] K. Balakrishnan, B. Brešar, M. Changar, W. Imrich, S. Klavžar, M. Kovše, A.R. Subhamathi, “On the remoteness function in median graphs,” Discrete Appl. Math., vol. 157, no. 18, pp. 3679–3688, 2009, doi: 10.1016/j.dam.2009.07.007.

[49] B. Brešar, M. Changat, J. Mathews, I. Peterin, P. G. Narasimha-Shenoi, and A. Tepeh Horvat, “Steiner intervals, geodesic intervals, and betweenness,” Discrete Math., vol. 309, no. 20, pp. 6114–6125, 2009, doi: 10.1016/j.disc.2009.05.022.

[48] B. Brešar and S. Špacapan, “Broadcast domination of products of graphs,” Ars Combin., vol. 92, pp. 303–320, 2009.

[47] B. Brešar and T. K. Šumenjak, “Cube intersection concepts in median graphs,” Discrete Math., vol. 309, no. 10, pp. 2990–2997, 2009, doi: 10.1016/j.disc.2008.07.032.

[46] B. Brešar and D. F. Rall, “Fair reception and Vizing’s conjecture,” J. Graph Theory, vol. 61, no. 1, pp. 45–54, 2009, doi: 10.1002/jgt.20366.

[45] B. Brešar and A. Tepeh Horvat, “Cage-amalgamation graphs, a common generalization of chordal and median graphs,” European J. Combin., vol. 30, no. 5, pp. 1071–1081, 2009, doi: 10.1016/j.ejc.2008.09.003.

[44] B. Brešar, M. Changat, S. Klavžar, J. Mathews, A. Mathews, and P. G. Narasimha-Shenoi, “Characterizing posets for which their natural transit functions coincide,” Ars Math. Contemp., vol. 2, no. 1, pp. 27–33, 2009, doi: 10.26493/1855-3974.72.9d1.

[43] B. Brešar, M. Changat, S. Klavžar, M. Kovše, J. Mathews, and A. Mathews, “Cover-incomparability graphs of posets,” Order, vol. 25, no. 4, pp. 335–347, 2008, doi: 10.1007/s11083-008-9097-1.

[42] B. Brešar, S. Klavžar, and A. T. Horvat, “On the geodetic number and related metric sets in Cartesian product graphs,” Discrete Math., vol. 308, no. 23, pp. 5555–5561, 2008, doi: 10.1016/j.disc.2007.10.007.

[41] B. Brešar and A. T. Horvat, “On the geodetic number of median graphs,” Discrete Math., vol. 308, no. 18, pp. 4044–4051, 2008, doi: 10.1016/j.disc.2007.07.119.

[40] B. Brešar and S. Špacapan, “On the connectivity of the direct product of graphs,” Australas. J. Combin., vol. 41, pp. 45–56, 2008.

[39] T. Bartnicki, B. Brešar, J. Grytczuk, M. Kovše, Z. Miechowicz, and I. Peterin, “Game chromatic number of Cartesian product graphs,” Electron. J. Combin., vol. 15, no. 1, p. Research Paper 72, 13, 2008, doi: 10.37236/796.

[38] B. Brešar, M. A. Henning, and D. F. Rall, “Rainbow domination in graphs,” Taiwanese J. Math., vol. 12, no. 1, pp. 213–225, 2008, doi: 10.11650/twjm/1500602498.

[37] B. Brešar and A. T. Horvat, “Crossing graphs of fiber-complemented graphs,” Discrete Math., vol. 308, no. 7, pp. 1176–1184, 2008, doi: 10.1016/j.disc.2007.04.005.

[36] B. Brešar, “Nonrepetitive sequences,” Obzornik Mat. Fiz., vol. 54, no. 3, pp. 73–80, 2007.

[35] B. Brešar and T. Kraner Šumenjak, “On the 2-rainbow domination in graphs,” Discrete Appl. Math., vol. 155, no. 17, pp. 2394–2400, 2007, doi: 10.1016/j.dam.2007.07.018.

[34] B. Brešar, S. Klavžar, and D. F. Rall, “On the packing chromatic number of Cartesian products, hexagonal lattice, and trees,” Discrete Appl. Math., vol. 155, no. 17, pp. 2303–2311, 2007, doi: 10.1016/j.dam.2007.06.008.

[33] B. Brešar and S. Špacapan, “Edge-connectivity of strong products of graphs,” Discuss. Math. Graph Theory, vol. 27, no. 2, pp. 333–343, 2007, doi: 10.7151/dmgt.1365.

[32] B. Brešar, M. A. Henning, and D. F. Rall, “Paired-domination of Cartesian products of graphs,” Util. Math., vol. 73, pp. 255–265, 2007.

[31] B. Brešar, S. Klavžar, and D. F. Rall, “Dominating direct products of graphs,” Discrete Math., vol. 307, no. 13, pp. 1636–1642, 2007, doi: 10.1016/j.disc.2006.09.013.

[30] B. Brešar and S. Klavžar, “Maximal proper subgraphs of median graphs,” Discrete Math., vol. 307, no. 11–12, pp. 1389–1394, 2007, doi: 10.1016/j.disc.2005.11.076.

[29] B. Brešar, P. Dorbec, S. Klavžar, and M. Mollard, “Hamming polynomials and their partial derivatives,” European J. Combin., vol. 28, no. 4, pp. 1156–1162, 2007, doi: 10.1016/j.ejc.2006.03.001.

[28] B. Brešar, “Characterizing almost-median graphs,” European J. Combin., vol. 28, no. 3, pp. 916–920, 2007, doi: 10.1016/j.ejc.2005.10.009.

[27] B. Brešar and S. Klavžar, “Crossing graphs as joins of graphs and Cartesian products of median graphs,” SIAM J. Discrete Math., vol. 21, no. 1, pp. 26–32, 2007, doi: 10.1137/050622997.

[26] B. Brešar, S. Klavžar, and R. Škrekovski, “On cube-free median graphs,” Discrete Math., vol. 307, no. 3–5, pp. 345–351, 2007, doi: 10.1016/j.disc.2004.09.018.

[25] B. Brešar, J. Grytczuk, S. Klavžar, S. Niwczyk, and I. Peterin, “Nonrepetitive colorings of trees,” Discrete Math., vol. 307, no. 2, pp. 163–172, 2007, doi: 10.1016/j.disc.2006.06.017.

[24] B. Brešar, M. A. Henning, and S. Klavžar, “On integer domination in graphs and Vizing-like problems,” Taiwanese J. Math., vol. 10, no. 5, pp. 1317–1328, 2006, doi: 10.11650/twjm/1500557305.

[23] B. Brešar and S. Klavžar, “Θ-graceful labelings of partial cubes,” Discrete Math., vol. 306, no. 13, pp. 1264–1271, 2006, doi: 10.1016/j.disc.2006.02.013.

[22] B. Brešar, S. Klavžar, and R. Škrekovski, “Roots of cube polynomials of median graphs,” J. Graph Theory, vol. 52, no. 1, pp. 37–50, 2006, doi: 10.1002/jgt.20146.

[21] B. Brešar, W. Imrich, and S. Klavžar, “Reconstructing subgraph-counting graph polynomials of increasing families of graphs,” Discrete Math., vol. 297, no. 1–3, pp. 159–166, 2005, doi: 10.1016/j.disc.2005.02.019.

[20] B. Brešar, W. Imrich, S. Klavžar, and B. Zmazek, “Hypercubes as direct products,” SIAM J. Discrete Math., vol. 18, no. 4, pp. 778–786, 2005, doi: 10.1137/S0895480103438358.

[19] B. Brešar, “Vizing-like conjecture for the upper domination of Cartesian products of graphs—the proof,” Electron. J. Combin., vol. 12, p. Note 12, 6, 2005, doi: 10.37236/1979.

[18] B. Brešar, P. K. Jha, S. Klavžar, and B. Zmazek, “Median and quasi-median direct products of graphs,” Discuss. Math. Graph Theory, vol. 25, no. 1–2, pp. 183–196, 2005, doi: 10.7151/dmgt.1271.

[17] B. Brešar, “On subgraphs of Cartesian product graphs and S-primeness,” Discrete Math., vol. 282, no. 1–3, pp. 43–52, 2004, doi: 10.1016/j.disc.2003.11.005.

[16] B. Brešar, S. Klavžar, A. Lipovec, and B. Mohar, “Cubic inflation, mirror graphs, regular maps, and partial cubes,” European J. Combin., vol. 25, no. 1, pp. 55–64, 2004, doi: 10.1016/j.ejc.2003.09.004.

[15] B. Brešar and S. Klavžar, “Square-free colorings of graphs,” Ars Combin., vol. 70, pp. 3–13, 2004.

[14] B. Brešar, W. Imrich, and S. Klavžar, “Tree-like isometric subgraphs of hypercubes,” Discuss. Math. Graph Theory, vol. 23, no. 2, pp. 227–240, 2003, doi: 10.7151/dmgt.1199.

[13] B. Brešar, “Arboreal structure and regular graphs of median-like classes,” Discuss. Math. Graph Theory, vol. 23, no. 2, pp. 215–225, 2003, doi: 10.7151/dmgt.1198.

[12] B. Brešar, W. Imrich, and S. Klavžar, “Fast recognition algorithms for classes of partial cubes,” in Discrete Appl. Math., vol. 131, 2003, pp. 51–61. doi: 10.1016/S0166-218X(02)00416-X.

[11] B. Brešar and B. Zmazek, “On the independence graph of a graph,” Discrete Math., vol. 272, no. 2–3, pp. 263–268, 2003, doi: 10.1016/S0012-365X(03)00194-8.

[10] B. Brešar, S. Klavžar, and R. Škrekovski, “Quasi-median graphs, their generalizations, and tree-like equalities,” European J. Combin., vol. 24, no. 5, pp. 557–572, 2003, doi: 10.1016/S0195-6698(03)00045-3.

[9] B. Brešar, S. Klavžar, and R. Škrekovski, “The cube polynomial and its derivatives: the case of median graphs,” Electron. J. Combin., vol. 10, p. Research Paper 3, 11, 2003, doi: 10.37236/1696.

[8] B. Brešar, “Intersection graphs of maximal hypercubes,” European J. Combin., vol. 24, no. 2, pp. 195–209, 2003, doi: 10.1016/S0195-6698(02)00142-7.

[7] B. Brešar and S. Klavžar, “On partial cubes and graphs with convex intervals,” Comment. Math. Univ. Carolin., vol. 43, no. 3, pp. 537–545, 2002.

[6] B. Brešar, W. Imrich, S. Klavžar, H. M. Mulder, and R. Škrekovski, “Tiled partial cubes,” J. Graph Theory, vol. 40, no. 2, pp. 91–103, 2002, doi: 10.1002/jgt.10031.

[5] B. Brešar, “The direct expansion of graphs,” in Discrete Math., vol. 244, 2002, pp. 17–30. doi: 10.1016/S0012-365X(01)00066-8.

[4] B. Brešar, “On the natural imprint function of a graph,” European J. Combin., vol. 23, no. 2, pp. 149–161, 2002, doi: 10.1006/eujc.2001.0555.

[3] B. Brešar, “On Vizing’s conjecture,” Discuss. Math. Graph Theory, vol. 21, no. 1, pp. 5–11, 2001, doi: 10.7151/dmgt.1129.

[2] B. Brešar, “Partial Hamming graphs and expansion procedures,” Discrete Math., vol. 237, no. 1–3, pp. 13–27, 2001, doi: 10.1016/S0012-365X(00)00362-9.

[1] B. Brešar, “On clique-gated graphs,” Discrete Math., vol. 199, no. 1–3, pp. 201–205, 1999, doi: 10.1016/S0012-365X(98)00305-7.