IBS/KAIST Joint Discrete Math Seminar

An odd [1,b]-factor in regular graphs from eigenvalues

Suil O (오수일)

Department of Applied Mathematics and Statistics, SUNY-Korea

Department of Applied Mathematics and Statistics, SUNY-Korea

2019/06/19 Wed 4:30PM-5:30PM

An odd [1,b]-factor of a graph is a spanning subgraph H such that for every vertex v∈V(G), 1≤d

_{H}(v)≤b, and d_{H}(v) is odd. For positive integers r≥3 and b≤r, Lu, Wu, and Yang gave an upper bound for the third largest eigenvalue in an r-regular graph with even number of vertices to guarantee the existence of an odd [1,b]-factor. In this talk, we improve their bound.