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- W2890968136 abstract "Let $a$ and $b$ be positive integers. An even $[a,b]$-factor of a graph $G$ is a spanning subgraph $H$ such that for every vertex $v in V(G)$, $d_H(v)$ is even and $a le d_H(v) le b$. Matsuda conjectured that if $G$ is an $n$-vertex 2-edge-connected graph such that $n ge 2a+b+frac{a^2-3a}b - 2$, $delta(G) ge a$, and $sigma_2(G) ge frac{2an}{a+b}$, then $G$ has an even $[a,b]$-factor. In this paper, we provide counterexamples, which are highly connected. Furthermore, we give sharp sufficient conditions for a graph to have an even $[a,b]$-factor. For even $an$, we conjecture a lower bound for $lambda_1(G)$ in an $n$-vertex graph to have an $[a,b]$-factor, where $lambda_1(G)$ is the largest eigenvalue of $G$." @default.
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- W2890968136 date "2018-09-14" @default.
- W2890968136 modified "2023-10-06" @default.
- W2890968136 title "Sharp conditions for the existence of an even $[a,b]$-factor in a graph." @default.
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