Suil O (오수일), An odd [1,b]-factor in regular graphs from eigenvalues

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.