路径因子涉及七阶和九阶路径
Path-factors involving paths of order seven and nine
摘要：
本文证明了以下两个定理（这里$c_{i}(G-X)$是具有$|V(C)|=i$的$G-X$的分支数$C$）：（i）如果图$G$对所有$X\subseteq V(G)$都满足$c_{1}(G-X)+\frac{1}{3}c_{3}(G-X)+\frac{1}{3}c_{5}(G-X)\leq \frac{2}{3}|X|$，则$G$有一个$\{P_{2},P_{7}\}$ -因子。(ii)~如果图$G$对所有$X\subseteq V(G)$都满足$c_{1}(G-X)+c_{3}(G-X)+\frac{2}{3}c_{5}(G-X)+\frac{1}{3}c_{7}(G-X)\leq \frac{2}{3}|X|$，则$G$有一个$\{P_{2},P_{9}\}$ -因子。
英文摘要：
In this paper, we show the following two theorems (here $c_{i}(G-X)$ is the number of components $C$ of $G-X$ with $|V(C)|=i$): (i)~If a graph $G$ satisfies $c_{1}(G-X)+\frac{1}{3}c_{3}(G-X)+\frac{1}{3}c_{5}(G-X)\leq \frac{2}{3}|X|$ for all $X\subseteq V(G)$, then $G$ has a $\{P_{2},P_{7}\}$-factor. (ii)~If a graph $G$ satisfies $c_{1}(G-X)+c_{3}(G-X)+\frac{2}{3}c_{5}(G-X)+\frac{1}{3}c_{7}(G-X)\leq \frac{2}{3}|X|$ for all $X\subseteq V(G)$, then $G$ has a $\{P_{2},P_{9}\}$-factor.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
