Algebraic Graph Theory - Wanting Sun

Title: Some results on spectral Turán's type problem

Abstract: It is well known that Turán's type problem is one of the most classical problems in graph theory. In this talk, we consider the spectral Turán's type problem. Let G be a graph and let F be a set of graphs, we say G is F-free if G does not contain any element of F as a subgraph. Firstly, we establish some spectral conditions to guarantee the non-existence of short odd cycles in a graph, which solves an open problem proposed by Lin, Ning and Wu. Then we introduce some new progress in determining the maximum spectral radius of an F-free graph with fixed number of edges. Joint work with Shuchao Li, Wei Wei, Yuantian Yu.