2-factors in claw-free graphs with locally disconnected vertices

Title:

2-factors in claw-free graphs with locally disconnected vertices

Creator:

An, Mingqiang, Xiong, Liming, and Tian, Runli

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a7e00b73-3397-4196-ae75-f54009eb77bf
uuid:a7e00b73-3397-4196-ae75-f54009eb77bf

Subject:

claw-free graph, 2-factor, closure, locally disconnected vertex, and singular edge

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

An edge of $G$ is singular if it does not lie on any triangle of $G$; otherwise, it is non-singular. A vertex $u$ of a graph $G$ is called locally connected if the induced subgraph $G[N(u)]$ by its neighborhood is connected; otherwise, it is called locally disconnected. In this paper, we prove that if a connected claw-free graph $G$ of order at least three satisfies the following two conditions: (i) for each locally disconnected vertex $v$ of degree at least $3$ in $G,$ there is a nonnegative integer $s$ such that $v$ lies on an induced cycle of length at least $4$ with at most $s$ non-singular edges and with at least $s-5$ locally connected vertices; (ii) for each locally disconnected vertex $v$ of degree $2$ in $G,$ there is a nonnegative integer $s$ such that $v$ lies on an induced cycle $C$ with at most $s$ non-singular edges and with at least $s-3$ locally connected vertices and such that $G[V (C)\cap V_{2} (G)]$ is a path or a cycle, then $G$ has a 2-factor, and it is the best possible in some sense. This result generalizes two known results in Faudree, Faudree and Ryjáček (2008) and in Ryjáček, Xiong and Yoshimoto (2010).

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

317-330

Source:

Czechoslovak Mathematical Journal | 2015 Volume:65 | Number:2

Harvested from:

CDK

Metadata only:

false