Induced claws and existence of even factors of graphs

Shengmei Lv; Liming Xiong; Guifu Su; Ning Zhao

doi:10.1007/s40840-016-0410-7

Induced claws and existence of even factors of graphs

Shengmei Lv, Liming Xiong^*, Guifu Su, Ning Zhao

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

An even factor of a graph G is a spanning subgraph in G such that the degree of each vertex is a positive even integer. In this paper, we show that for any induced claw of simple graph G of order at least 10, if there exists at least a pair of vertices out of the claw such that they are the common neighbors of nonadjacent vertices of the claw, then G has an even factor if and only if δ(G) ≥ 2 and every odd branch-bond of G contains a branch of length 1. The even factor of claw-heavy graphs was also characterized.

Original language	English
Pages (from-to)	1529-1540
Number of pages	12
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	41
Issue number	3
DOIs	https://doi.org/10.1007/s40840-016-0410-7
Publication status	Published - 1 Jul 2018

Keywords

Branch-bond
Claw-heavy graph
Even factor
Even subgraph
Induced claw

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10.1007/s40840-016-0410-7

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AU - Xiong, Liming

AU - Su, Guifu

AU - Zhao, Ning

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N2 - An even factor of a graph G is a spanning subgraph in G such that the degree of each vertex is a positive even integer. In this paper, we show that for any induced claw of simple graph G of order at least 10, if there exists at least a pair of vertices out of the claw such that they are the common neighbors of nonadjacent vertices of the claw, then G has an even factor if and only if δ(G) ≥ 2 and every odd branch-bond of G contains a branch of length 1. The even factor of claw-heavy graphs was also characterized.

AB - An even factor of a graph G is a spanning subgraph in G such that the degree of each vertex is a positive even integer. In this paper, we show that for any induced claw of simple graph G of order at least 10, if there exists at least a pair of vertices out of the claw such that they are the common neighbors of nonadjacent vertices of the claw, then G has an even factor if and only if δ(G) ≥ 2 and every odd branch-bond of G contains a branch of length 1. The even factor of claw-heavy graphs was also characterized.

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KW - Claw-heavy graph

KW - Even factor

KW - Even subgraph

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Induced claws and existence of even factors of graphs

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Keywords

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