The existence of a path-factor without small odd paths

Abstract

In this paper, we show that if a graph $G$ satisfies $c_1(G-X)+\frac{2}{3}{c}_3(G-X)\le \frac{4}{3}|X|+\frac{1}{3}$ for all $X\subseteq V(G)$, then $G$ has a $\{P_2,P_5\}$-factor, where $c_i(G-X)$ is the number of components $C$ of $G-X$ with $|V(C)|=i$.

arXiv comment23 pages, 5 figures

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