论文标题
具有所有（分数）$ [a，b] $的图形的光谱条件 - 因素
Spectral conditions for graphs having all (fractional) $[a,b]$-factors
论文作者
论文摘要
令$ a \ leq b $为两个正整数。我们说，图$ g $具有所有$ [a，b] $ - 如果每个函数都有$ h $ factor $ h：v（g）\ rightarrow \ mathbb {z}^+$，以便所有$ a \ le h（v）\ le h（v）\ le b $ in V（g）$和$ \ sum_ qu \ sum_ emod que（v） 2 $，并且具有所有分数$ [a，b] $ - 如果每个$ p：v（g）\ rightArrow \ mathbb {z}^+$具有分数$ p $ factor，则$ a \ le p（v）\ le p（v）\ le B $ in V（g）$ in v（g）$。在本文中，我们为所有$ [a，b] $ - 因子（$ 3 \ leq a <b $）和所有分数$ [a，b] $ - 因子（$ 1 \ leq a <b $）提供了紧密的光谱半径条件。
Let $a\leq b$ be two positive integers. We say that a graph $G$ has all $[a,b]$-factors if it has an $h$-factor for every function $h: V(G)\rightarrow \mathbb{Z}^+$ such that $a\le h(v) \le b$ for all $v\in V(G)$ and $\sum_{v\in V(G)}h(v)\equiv 0\pmod 2$, and has all fractional $[a,b]$-factors if it has a fractional $p$-factor for every $p: V(G) \rightarrow \mathbb{Z}^+$ such that $a\le p(v)\le b$ for all $v\in V(G)$. In this paper, we provide tight spectral radius conditions for graphs having all $[a,b]$-factors ($3\leq a<b$) and all fractional $[a,b]$-factors ($1\leq a<b$), respectively.
