Two operations on a graph preserving the (non)existence of 2-factors in its line graph

An, Mingqiang, et al. "Two operations on a graph preserving the (non)existence of 2-factors in its line graph." Czechoslovak Mathematical Journal 64.4 (2014): 1035-1044. <http://eudml.org/doc/269841>.

@article{An2014,
abstract = {Let $G=(V(G),E(G))$ be a graph. Gould and Hynds (1999) showed a well-known characterization of $G$ by its line graph $L(G)$ that has a 2-factor. In this paper, by defining two operations, we present a characterization for a graph $G$ to have a 2-factor in its line graph $L(G).$ A graph $G$ is called $N^\{2\}$-locally connected if for every vertex $x\in V(G),$$G[\lbrace y\in V(G)\; 1\le \{\rm dist\}_\{G\}(x,y)\le 2\rbrace ]$ is connected. By applying the new characterization, we prove that every claw-free graph in which every edge lies on a cycle of length at most five and in which every vertex of degree two that lies on a triangle has two $N^\{2\}$-locally connected adjacent neighbors, has a $2$-factor. This result generalizes the previous results in papers: Li, Liu (1995) and Tian, Xiong, Niu (2012), and is the best possible.},
author = {An, Mingqiang, Lai, Hong-Jian, Li, Hao, Su, Guifu, Tian, Runli, Xiong, Liming},
journal = {Czechoslovak Mathematical Journal},
keywords = {2-factor; claw-free graph; line graph; $N^\{2\}$-locally connected; 2-factor; claw-free graph; line graph; $N^\{2\}$-locally connected},
language = {eng},
number = {4},
pages = {1035-1044},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Two operations on a graph preserving the (non)existence of 2-factors in its line graph},
url = {http://eudml.org/doc/269841},
volume = {64},
year = {2014},
}

TY - JOUR
AU - An, Mingqiang
AU - Lai, Hong-Jian
AU - Li, Hao
AU - Su, Guifu
AU - Tian, Runli
AU - Xiong, Liming
TI - Two operations on a graph preserving the (non)existence of 2-factors in its line graph
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 4
SP - 1035
EP - 1044
AB - Let $G=(V(G),E(G))$ be a graph. Gould and Hynds (1999) showed a well-known characterization of $G$ by its line graph $L(G)$ that has a 2-factor. In this paper, by defining two operations, we present a characterization for a graph $G$ to have a 2-factor in its line graph $L(G).$ A graph $G$ is called $N^{2}$-locally connected if for every vertex $x\in V(G),$$G[\lbrace y\in V(G)\; 1\le {\rm dist}_{G}(x,y)\le 2\rbrace ]$ is connected. By applying the new characterization, we prove that every claw-free graph in which every edge lies on a cycle of length at most five and in which every vertex of degree two that lies on a triangle has two $N^{2}$-locally connected adjacent neighbors, has a $2$-factor. This result generalizes the previous results in papers: Li, Liu (1995) and Tian, Xiong, Niu (2012), and is the best possible.
LA - eng
KW - 2-factor; claw-free graph; line graph; $N^{2}$-locally connected; 2-factor; claw-free graph; line graph; $N^{2}$-locally connected
UR - http://eudml.org/doc/269841
ER -