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

Room B232 IBS (기초과학연구원)

An odd $$-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

Suil O (오수일), Eigenvalues and [a, b]-factors in regular graphs

Room B232 IBS (기초과학연구원)

For positive integers, $r \ge 3, h \ge 1,$ and $k \ge 1$, Bollobás, Saito, and Wormald proved some sufficient conditions for an $h$-edge-connected $r$-regular graph to have a k-factor in 1985. Lu gave an upper bound for the third-largest eigenvalue in a connected $r$-regular graph to have a $k$-factor in 2010. Gu found an upper bound

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