COSAM » Events » 2018 » January » DMS Colloquium: Dr. Songling Shan

 DMS Colloquium: Dr. Songling Shan Time: Jan 29, 2018 (04:00 PM) Location: Parker Hall 250 Details: Speaker: Dr. Songling Shan, Vanderbilt University Title: Chvátal's Toughness Conjecture and Related Problems Abstract: Introduced by Chvátal in 1973, toughness is a measure of graph connectivity and "resilience'' under removal of vertices. It is well known that every cycle is 1-tough. Conversely, Chvátal conjectured that there is a constant $t_0$ such that every $t_0$-tough graph contains a Hamiltonian cycle (Chvátal's Toughness Conjecture). The construction of Bauer, Broersma, and Veldman in 2000 shows that $t_0$ should be at least $\frac{9}{4}$ if exists.  In this talk, I will survey  progress toward  Chvátal's Toughness Conjecture and results about toughness conditions that guarantee the existence of more general spanning structures in a graph.

Last updated: 01/16/2018