A $\{P_{2},P_{5}\}$-factor of a graph is a spanning subgraph of the graph each of whose components is isomorphic to either $P_{2}$ or $P_{5}$, where $P_{n}$ denote the path of order $n$. In this paper, we show that if a graph $G$ satisfies $c_{1}(G-X)+\frac{2}{3}c_{3}(G-X)\leq \frac{4}{3}|X|+\frac{1}{3}$ 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 $|V(C)|=i$. Moreover, it is shown that above condition is sharp.
@article{10_37236_5817,
author = {Yoshimi Egawa and Michitaka Furuya},
title = {The existence of a path-factor without small odd paths},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {1},
doi = {10.37236/5817},
zbl = {1391.05204},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5817/}
}
TY - JOUR
AU - Yoshimi Egawa
AU - Michitaka Furuya
TI - The existence of a path-factor without small odd paths
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/5817/
DO - 10.37236/5817
ID - 10_37236_5817
ER -
%0 Journal Article
%A Yoshimi Egawa
%A Michitaka Furuya
%T The existence of a path-factor without small odd paths
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/5817/
%R 10.37236/5817
%F 10_37236_5817
Yoshimi Egawa; Michitaka Furuya. The existence of a path-factor without small odd paths. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/5817
