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 $v\in V(G)$, $1\le d_H(v)\le b$, and $d_H(v)$ is odd. For positive integers $r\ge 3$ and $b\le r$, 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.