论文标题
具有所有$（a，b）$ - 均等因素的图表条件
A Degree Condition for Graphs Having All $(a,b)$-Parity Factors
论文作者
论文摘要
令$ a $和$ b $为正整数，以便$ a \ leq b $和$ a \ equiv b \ pmod 2 $。我们说$ g $具有所有$（a，b）$ - 平价因素，如果$ g $具有$ h $ factor $ h：v（g）\ rightArrow \ {a，a+2，a+2，\ ldots，b-2，b \} $，带有$ b | v（g）| $ heve and $ h（v）和$ h（v）\ equiv b \ equiv b \ equ b \ p $ v $ v。在本文中，我们证明，$ n \ geq 3（b+1）（a+b）$ vertices具有所有$（a，b）$ - 平等因素，如果$δ（g）\ geq（b^2-b）/a $，对于任何两个非adjacent thjacent $ u，in（b^2-b）/a $ $ \ max \ {d_g（u），d_g（v）\} \ geq \ frac {bn} {a+b} $。此外，我们表明，从某种意义上说，这个结果是最好的。
Let $a$ and $b$ be positive integers such that $a\leq b$ and $a\equiv b\pmod 2$. We say that $G$ has all $(a, b)$-parity factors if $G$ has an $h$-factor for every function $h: V(G) \rightarrow \{a,a+2,\ldots,b-2,b\}$ with $b|V(G)|$ even and $h(v)\equiv b\pmod 2$ for all $v\in V(G)$. In this paper, we prove that every graph $G$ with $n\geq 3(b+1)(a+b)$ vertices has all $(a,b)$-parity factors if $δ(G)\geq (b^2-b)/a$, and for any two nonadjacent vertices $u,v \in V(G)$, $\max\{d_G(u),d_G(v)\}\geq \frac{bn}{a+b}$. Moreover, we show that this result is best possible in some sense.
