Events
DMS Combinatorics Seminar |
Time: Sep 11, 2024 (12:55 PM) |
Location: 328 Parker Hall |
Details: Speaker: Arthur Tanyel (Auburn University) Title: Degree sequence condition for Hamiltonicity in tough graphs Abstract: Generalizing both Dirac's condition and Ore's condition for Hamilton cycles, Chvátal in 1972 established a degree sequence condition for the existence of a Hamilton cycle in a graph. Hoàng in 1995 generalized Chvátal's degree sequence condition for 1-tough graphs and conjectured a t-tough analogue for any positive integer t≥1. Hoàng in the same paper verified his conjecture for t≤3 and recently Hoàng and Robin verified the conjecture for t=4. In this talk, we present a proof of the conjecture for all t≥4. The proof depends on two newly established results on cycle structures in tough graphs, which hold independent interest. |