Research
My research is in Graph Theory and Partially Ordered Sets.
A copy of my CV from August 2021 is available here:
Book
Tolerance Graphs (with M.C. Golumbic), Cambridge University Press, 2004.
Book Chapter
Split Graphs (with K. L. Collins), in Topics in Algorithmic Graph Theory, L. Beineke, M. C. Golumbic, and R. Wilson editors, Encyclopedia of Mathematics and its Applications 178, Cambridge University Press, 189-206, 2021.
Recent Work
The distinguishing number and distinguishing chromatic number for posets (with K. Collins), submitted.
https://arxiv.org/abs/1905.09858
Dimension of restricted classes of interval orders (with M.T. Keller and S.J. Young), submitted.
https://arxiv.org/abs/2004.08294
Product throttling for power domination, (with S.E. Anderson, K.L. Collins, D. Ferrero, L. Hogben, C. Meyer, and S. Walker), submitted.
Publications in Graph Theory and Partially Ordered Sets
39. Product throttling, (with S.E. Anderson, K.L. Collins, D. Ferrero, L. Hogben, C. Meyer, and S. Walker). To appear in Research Trends in Graph Theory and Applications, D. Ferraro, L. Hogben, S. Kingan, G. L. Matthews editors, Association for Women in Mathematics Series, Springer. https://arxiv.org/abs/2012.12807
38. Interval orders with two interval lengths, (with S. Boyadzhiyska and G. Isaak), Discrete Applied Math., Vol. 267, 52-63 (2019). arXiv:1707.08093
37. Finding balance: Split graphs and related classes, (with K. Collins), Electronic Journal of Combinatorics, Vol. 25 (1), #P1.73 (2018). https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i1p73
36. Tolerance orders of open and closed intervals, (with A. Shuchat and R. Shull), ORDER, Vol. 36 (2), 313--333 (2019). arXiv:1707.08099
35. A simple proof characterizing interval orders with interval lengths between 1 and $k$ (with S. Boyadzhiyska and G. Isaak), Involve Vol. 11(5), 893-900 (2018). arXiv:1709.00313
34. Split graphs and Nordhaus-Gaddum graphs, (with C. Cheng and K. Collins), Discrete Math., Vol. 339 (9), 2345--2356 (2016). arXiv:1506.03746
33. Unit Interval Orders of Open and Closed Intervals, (with A. Shuchat and R. Shull), ORDER, Vol 33(1), 85--99 (2016). arXiv.org/abs/1501.06430
32. Unit Mixed Interval Graphs, (with A. Shuchat, R. Shull and L. West '11), Congressus Numerantium, Vol 221, 189--223 (2014). arXiv:1405.4247
31. Nordhaus-Gaddum Theorem for the Distinguishing Chromatic Number, (with K. Collins), Electronic Journal of Combinatorics, Vol. 20 (3), \#P46 (2013) https://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i3p46
30. Fractional weak discrepancy and split semiorders, (with A. Shuchat and R. Shull), Discrete Applied Math. Vol. 159(7), 647--660 (2011).
29. The total weak discrepancy of a partially ordered set, (with A. Shuchat and R. Shull), Ars. Mathematica Contemporanea, Vol. 4: 95--109 (2011).
28. The t-discrepancy of a poset, (with D. Howard), Discrete Applied Math., Vol. 158(16), 1789--1798 (2010).
27. The total linear discrepancy of an ordered set, (with D. Howard, R. Shull, and N. Streib), Discrete Math., Vol. 310(5), 1022--1025 (2010).
26. Bounds on the distinguishing chromatic number, (with K. Collins and M. Hovey), Electronic Journal of Combinatorics, Vol. 16(1), \#R88 (2009). https://www.combinatorics.org/ojs/index.php/eljc/article/view/v16i1r88
25. Fractional weak discrepancy and interval orders, (with A. Shuchat and R. Shull), Discrete Applied Math. Vol. 157, 1873--1884 (2009).
24. Fractional weak discrepancy of posets and certain forbidden configurations, (with A. Shuchat and R. Shull), in The Mathematics of Preference, Choice, and Order, Springer, Berlin, 291--301 (2009).
23. The fractional weak discrepancy of a partially ordered set, (with A. Shuchat and R. Shull), Discrete Applied Math. Vol. 155, 2227--2235 (2007).
22. The distinguishing chromatic number, (with K. Collins), Electronic Journal of Combinatorics, Vol. 13(1), \#R16 (2006). https://www.combinatorics.org/ojs/index.php/eljc/article/view/v13i1r16
21. Range of the fractional weak discrepancy function, (with A. Shuchat and R. Shull), ORDER Vol. 23, 51--63 (2006).
20. A hierarchy of classes of bounded bitolerance orders, (with G. Isaak and K. Nyman), ARS Combinatoria Vol. 69, 33--53 (2003).
19. Archimedean phi-tolerance graphs, (with M.C. Golumbic and R. Jamison), J. Graph Theory, Vol. 41, 179--194 (2002).
18. Interval digraphs and bounded bitolerance digraphs (with R. Shull), Congressus Numerantium, Vol. 151, 111--127 (2001).
17. Comparability invariance results for tolerance orders, (with K.P. Bogart, G. Isaak and J. Laison), ORDER, Vol. 18(3), 281--294 (2001).
16. Linear discrepancy and bandwidth, (with P.C. Fishburn and P.J. Tanenbaum), ORDER, Vol. 18(3), 237--245 (2001).
15. Linear discrepancy and weak discrepancy of an ordered set, (with P.C. Fishburn and P.J. Tanenbaum), ORDER, Vol. 18(3), 201--225 (2001).
14. Bounded bitolerance digraphs, (with K. P. Bogart), Discrete Math., Vol. 215, 13--20 (2000).
13. Stack and queue layouts of directed acyclic graphs: Part I, (with L. S. Heath and S. R. Pemmaraju), SIAM Journal on Computing, Vol. 28, 1510--1539 (1999). Extended abstract appeared in DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 9, 5--11 (1993).
12. On the fractional intersection number of graphs, (with E.R. Scheinerman), Graphs and Combinatorics, Vol. 15, 341--351 (1999).
11. On the weakness of an ordered set, (with J.G. Gimbel), SIAM Journal on Discrete Math., Vol. 11, No. 4, 655--663 (1998).
10. On k-weak orders: Recognition and a tolerance result, Discrete Mathematics, Vol. 181, 223--237 (1998).
9. Dot product representations of graphs, (with C.M. Fiduccia, E.R. Scheinerman, and J. Zito), Discrete Mathematics, Vol. 181, 113--138 (1998).
8. Cliques that are tolerance digraphs, (with R. Shull), Discrete Applied Math., Vol. 80, 119--134 (1997).
7. Unit and proper bitolerance digraphs, (with R. Shull), Journal of Graph Theory, Vol. 24, No. 2, 193--199 (1997).
6. Trees and Cycles that are bounded bitolerance digraphs, (with K. P. Bogart), Congressus Numerantium, Vol. 112, 17--32, (1995).
5. On point-halfspace graphs, (with E. R. Scheinerman and D. Ullman), Journal of Graph Theory, Vol. 20, 19--35 (1995).
4. Generalized perfect graphs: characterizations and inversion, Discrete Applied Mathematics, Vol. 60, 359--387 (1995)
3. Bipartite tolerance orders, (with K. P. Bogart), Discrete Mathematics, Vol. 132, 11--22 (1994).
2. On generalized perfect graphs: bounded degree and bounded edge perfection, (with E. R. Scheinerman), Discrete Applied Mathematics, Vol. 44, 233--245 (1993).
1. On generalized perfect graphs: alpha-perfection and acyclic chi-perfection, (with E. R. Scheinerman), Congressus Numerantium, Vol. 79, 163--172 (1990).