Casey Tompkins

Office hour for students:

Room: 1.045
Kollegiengebäude Mathematik (20.30)

Email: Casey.Tompkins@kit.edu

I work in combinatorics, particularly on extremal problems. A major topic of my research is finding hypergraph generalizations of classical results in graph theory. I was born in Chicago and did my undergraduate studies at Lake Forest College. After participating in the Budapest Semesters in Mathematics program, I went on to do my masters and Ph.D. studies at Central European University in Budapest, Hungary. Under the guidance of Gyula O.H. Katona, I wrote my dissertation on extremal problems for partially ordered sets. Afterword, I held a Young Researcher position at the Alfréd Rényi Institute of Mathematics, and I am now a postdoc at the Karlsruhe Institute of Technology, working with Maria Axenovich.

Semester

Titel

Typ

Publications:

1. E. Győri, A. Methuku, N. Salia, C. Tompkins, M. Vizer. On the maximum number of hyperedges in connected hypergraphs without long paths. Discrete Mathematics 341(9), 2602–2605, 2018.

2. D. Grósz, A. Methuku, and C. Tompkins. An upper bound on the size of diamond-free families of sets. Journal of Combinatorial Theory, Series A 156, 164–194, 2018.

3. A. Davoodi, E. Győri, A. Methuku, C. Tompkins. An Erdős-Gallai type theorem for hypergraphs. European Journal of Combinatorics 69, 159–162, 2018.

4. D. Gerbner, A. Methuku, C. Tompkins. Intersecting P-free families. Journal of Combinatorial Theory, Series A 151, 61–83, 2017.

5. P. Aboulker, G. Lagarde, D. Malec, A. Methuku, C. Tompkins. De Bruijn-Erdős type theorems for graphs and posets. Discrete Mathematics 340(5), 995–999, 2017.

6. D. Grósz, A. Methuku, and C. Tompkins. An improvement of the general bound on the largest family of subsets avoiding a subposet. Order 34, 113–125, 2016.

7. A. Methuku and C. Tompkins. Exact forbidden subposet results using chain decompositions of the cycle. The Electronic Journal of Combinatorics, 22(4), 2015.

8. E. Győri, S. Kensell, C. Tompkins. Making a C6-free graph C4-free and bipartite. Discrete Applied Mathematics 209, 133–136, 2015.

9. D. Grósz, A. Methuku, and C. Tompkins. Uniformity thresholds for the asymptotic size of extremal Berge-F-free hypergraphs. Electronic Notes in Discrete Mathematics 61, 527–533, 2017. (extended abstract).

10. E. Győri, D. Korándi, A. Methuku, I. Tomon, C. Tompkins, M. Vizer. On the Turán number of some ordered even cycles. European Jounal of Combinatorics, accepted.

11. J. Cardinal, S, Felsner, T. Miltzow, C. Tompkins, B. Vogtenhuber. Intersection graphs of rays and grounded segments. Journal of Graph Algorithms and Applications, accepted (also appeared in a peer reviewed conference WG 2017).

12. E. Győri, G. Katona, L. Papp, C. Tompkins. The optimal pebbling number of staircase graphs. Discrete Mathematics, accepted.

13. D. Grósz, A. Methuku, C. Tompkins. On subgraphs of C2k-free graphs and a problem of Kühn and Osthus. arXiv:1708.05454, submitted.

14. G. Bacsó, Cs. Bujtás, C. Tompkins, Zs. Tuza. Disjoint total dominating sets in 3-regular graphs, submitted.

15. C. Tompkins and Y. Wang. On an extremal problem involving a pair of forbidden posets. arXiv:1710.10760, submitted.

16. M. Ferrara, D. Johnston, S. Loeb, F. Pfender, A. Schulte, H. Smith, E. Sullivan, M. Tait, C. Tompkins. On Edge-Colored Saturation Problems. arXiv:1712.00163, submitted.

17. N. Salia, C. Tompkins, O. Zamora. An Erdős-Gallai type theorem for vertex colored graphs. To appear in Discrete Mathematics.

18. E. Győri, N. Salia, C. Tompkins, O. Zamora. The maximum number of Pl copies in Pk-free graphs. arXiv:1803.03240, submitted.

19. B. Ergemlidze, E. Győri, A. Methuku, C. Tompkins, O. Zamora. Avoiding long Berge cycles, the missing cases k = r + 1 and k = r + 2. arXiv:1808.09863, submitted.

20. N. Salia, C. Tompkins, Z. Wang, O. Zamora. Ramsey numbers of Berge hypergraphs and related structures. arXiv:1808.07687, submitted.

**Research Group on Discrete Mathematics**

**Secretariat**

Kollegiengebäude Mathematik (20.30)

Room 1.044

**Address**

Institut für Algebra und Geometrie

Englerstr. 2

D-76131 Karlsruhe

**Office hours:**

Tu, Th, F 8:30-12:00

**Tel.:** +49 721 608 47412

**Fax.:** +49 721 608 46968