Research

Mathematical Research

• Areas of study according to AMS: 52-xx Convex and Discrete Geometry, 51-xx Geometry, 05-xx Combinatorics.

1. D. Lara, C. Rubio-Montiel and F. Zaragoza; On Grundy indices for complete geometric graphs, arXiv:2510.15155.

2. M. Olsen, C. Rubio-Montiel and A. Silva-Ramírez; Acyclic and complete coloring of digraphs with the minimum and maximum possible numbers of colors, arXiv:2508.16043.

3. N. Javier-Nol, C. Rubio-Montiel and I. Torres-Ramos; The dib-chromatic number of digraphs, arXiv:2411.14248.

4. J. Cervantes-Ojeda, M. C. Gómez-Fuentes and C. Rubio-Montiel; Genetic algorithm and edge-colorings of complete graphs with connected classes, submitted for publication, arXiv:2405.01811.

5. M. Abreu, J. B. Gauci, D. Mattiolo, G. Mazzuoccolo, F. Romaniello, C. Rubio-Montiel and T. Traetta; A sharp upper bound for the harmonious total chromatic number of graphs and multigraphs, Art. Discrete Appl. Math., 8(3):#P3.02,10pp, 2025.

6. M. Buratti, F. Merola, A. Nakic and C. Rubio-Montiel; Banff designs: difference methods for coloring incidence graphs, Art. Discrete Appl. Math., 8(3):#P3.01,11pp, 2025.

7. M. Olsen, C. Rubio-Montiel and A. Silva-Ramírez; Zykov sums of digraphs with diachromatic number equal to their harmonious chromatic number, Discrete Math. Lett., 14(1):7-12, 2024.

8. G. Araujo-Pardo, J. J. Montellano-Ballesteros, M. Olsen and C. Rubio-Montiel; On the harmonious chromatic number of graphs, Bol. Soc. Mat. Mex. (3), 30(2):Paper No. 59,16pp, 2024.

9. C. Alfaro, C. Rubio-Montiel and A. Vázquez-Ávila; Covering and 2-degree-packing numbers in graphs, Open J. Discrete Appl. Math., 7(1):1-10, 2024.

10. G. Araujo-Pardo and C. Rubio-Montiel; Achromatic arboricity on complete graphs, Aequat. Math., 98:1-12, 2024.

11. C. Rubio-Montiel; Extremal regular graphs of given chromatic number, Ars Combin., 157:133-141, 2023.

12. A. Atilano, S. Bejos and C. Rubio-Montiel; Motions of a connected subgraph representing a swarm of robots inside a graph of work stations, Electron. J. Graph Theory Appl., 10(2):501-521, 2022.

13. G. Araujo-Pardo, J. J. Montellano-Ballesteros, M. Olsen and C. Rubio-Montiel; The digrundy number of digraphs, Discrete Appl. Math., 317:117-123, 2022.

14. G. Araujo-Pardo, J. C. Díaz and C. Rubio-Montiel; Achromatic number of Kneser graphs, Ars Math. Contemp., 21(1):#P1.05,13pp, 2021.

15. G. Araujo-Pardo, Gy. Kiss, C. Rubio-Montiel and A. Vázquez-Ávila; On line colorings of finite projective spaces, Graphs Combin., 37(3):891-905, 2021.

16. G. Araujo-Pardo, J. J. Montellano-Ballesteros, M. Olsen and C. Rubio-Montiel; Achromatic numbers for circulant graphs and digraphs, Discuss. Math. Graph Theory, 41(3):713-724, 2021.

17. C. Rubio-Montiel; On the 4-girth-thickness of the line graph of the complete graph, Util. Math., 117:107-112, 2020. arXiv:1804.08723.

18. H. Castañeda-López, P.C. Palomino, A.B. Ramos-Tort, C. Rubio-Montiel and C. Silva-Ruiz; The 6-girth-thickness of the complete graph, AKCE Int. J. Graphs Comb., 17(3):856-861, 2020.

19. C. Alfaro, G. Araujo-Pardo, C. Rubio-Montiel and A. Vázquez-Ávila; On transversal and 2-packing numbers in uniform linear systems, AKCE Int. J. Graphs Comb., 17(1):335-341, 2020.

20. C. Alfaro, C. Rubio-Montiel and A. Vázquez-Ávila; On two-quotient strong starters for Fq, Util. Math., 112:287-302, 2019. ArXiv:1609.05496.

21. C. Huemer, D. Lara and C. Rubio-Montiel; Coloring decompositions of complete geometric graphs, Acta Math. Hungar., 159(2), 429-446, 2019.

22. C. Rubio-Montiel; The 4-girth-thickness of the complete multipartite graph, Electron. J. Graph Theory Appl., 7(1):183-188, 2019.

23. D. Lara and C. Rubio-Montiel; On crossing families of complete geometric graphs, Acta Math. Hungar., 157(2), 301-311, 2019.

24. G. Araujo-Pardo, F. E. Contreras-Mendoza, S. J. Murillo-García, A. B. Ramos-Tort and C. Rubio-Montiel; Complete colorings of planar graphs, Discrete Appl. Math., 255:86-97, 2019.

25. G. Araujo-Pardo, C. Rubio-Montiel and A. Vázquez-Ávila; A note on the Erdös-Faber-Lovász conjecture: quasigroups and complete digraphs, Ars Comb., 143:53-57, 2019.

26. G. Araujo-Pardo, Gy. Kiss, C. Rubio-Montiel and A. Vázquez-Ávila; On chromatic indices of finite affine spaces, Ars Math. Contemp., 16(1):67-79, 2019.

27. C. Rubio-Montiel; La multifacética conjetura de Erdős, Fáber y Lóvasz, Miscelánea Mat., 67:43-56, 2019.

28. G. Araujo-Pardo and C. Rubio-Montiel; On ωψ-perfect graphs, Ars Combin., 141:375-387, 2018.

29. G. Araujo-Pardo, J. J. Montellano-Ballesteros, M. Olsen and C. Rubio-Montiel; The diachromatic number of digraphs, Electron. J. Combin., 25(3):#P3.51,17pp, 2018.

30. C. Rubio-Montiel; The 4-girth thickness of the complete graph, Ars Math. Contemp., 14(2):319-327, 2018.

31. G. Araujo-Pardo, J. J. Montellano-Ballesteros, C. Rubio-Montiel and R. Strausz; On the pseudoachromatic index of the complete graph III, Graphs Combin., 34(2):277-287, 2018.

32. G. Araujo-Pardo and C. Rubio-Montiel; Pseudoachomatic and connected-pseudoachromatic indices of the complete graph, Discrete Appl. Math., 231:60-66, 2017.

33. C. Rubio-Montiel; The Hadwiger number, chordal graphs and ab-perfection, AKCE Int. J. Graphs Comb., 14(2):130-134, 2017.

34. O. Aichholzer, G. Araujo-Pardo, N. García-Colín, T. Hackl, D. Lara, C. Rubio-Montiel and J. Urrutia; Geometric achromatic and pseudoachromatic indices, Graphs Combin., 32(2):431-451, 2016.

35. G. Araujo-Pardo, J. C. Díaz and C. Rubio-Montiel; The achromatic number of Kneser graphs, In Discrete Mathematics Days - JMDA16, 54 of Electron. Notes Discrete Math., pages 253-258. Elsevier Sci. B. V., Amsterdam, 2016.

36. C. Rubio-Montiel; A new characterization of trivially perfect graphs, Electron. J. Graph Theory Appl., 3(1):22-26, 2015.

37. Gy. Kiss and C. Rubio-Montiel; A note on m-factorizations of complete multigraphs arising from designs, Ars Math. Contemp., 8(1):163-175, 2015.

38. D. Lara, C. Rubio-Montiel and F. Zaragoza; Grundy and pseudo-Grundy indices for geometric graphs, In Abstracts of the XVI Spanish Meeting on Computational Geometry, pages 73-76, Barcelona, Spain, July 2015.

39. G. Araujo-Pardo, J. J. Montellano-Ballesteros, C. Rubio-Montiel and R. Strausz; On the pseudoachromatic index of the complete graph II, Bol. Soc. Mat. Mex. (3), 20(1):17-28, 2014.

40. G. Araujo-Pardo and C. Rubio-Montiel; On ωψ-perfection of graphs, In The VII Latin-American Algorithms, Graphs, and Optimization Symposium, 44 of Electron. Notes Discrete Math., pages 163-168. Elsevier Sci. B. V., Amsterdam, 2013.

Research visits

• Posdoc at UMI LAFMIA 3175 CNRS, CINVESTAV-IPN, Mexico City. Advisor: Carlos Coello PhD. From March 2017 to July 2017.

• Posdoc at Comenius University, Bratislava, Slovakia. Adviser: Robert Jajcay, PhD. From January 2016 to December 2016. Video.

• Polytechnic University of Catalonia, Barcelona, Spain. Local adviser: Camino Balbuena, PhD. From September 2013 to February 2014.

• Eötvös Lórand University, Budapest, Hungary. Local adviser: György Kiss, PhD. From September 2012 to February 2013.

Grants awarded

• Project PAIDI/007/21 "Colorings of graphs and digraphs" 2021-2022.

• Project PAIDI/007/19 "Colorings and thickness of graphs" 2019-2020.