Speaker: Xinyi Xu, an independent researcher, received a PhD in Mathematics from London School of Economics in 2023.

Date: July 15, 2024

Time: 15:00-16:00

Location: Zoom Meeting: 981 4604 9841

Sponsor: School of Mathematics, Shandong University

Abstract:

If a graph is n-colourable, then it obviously is n'-colourable for any n' ≥ n. But the situation is not so clear when we consider multi-colourings of graphs. A graph is (n,k)-colourable if we can assign each vertex a k-subset of {1,2,...,n} so that adjacent vertices receive disjoint subsets. We consider the following problem: if a graph is (n,k)-colourable, then for what pairs (n', k') is it also (n',k')-colourable? This question can be translated into a question regarding multi-colourings of Kneser graphs, for which Stahl formulated a conjecture in 1976. We present new results, strengthen existing results, and in particular present much simpler proofs of several known cases of the conjecture.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/193544.htm