Star subdivisions and connected even factors in the square of a graph

Jan Ekstein; Pemysl Holub; Tomáš Kaiser; Liming Xiong; Shenggui Zhang

doi:10.1016/j.disc.2011.09.004

Star subdivisions and connected even factors in the square of a graph

Jan Ekstein
, Pemysl Holub^*
, Tomáš Kaiser
, Liming Xiong
, Shenggui Zhang

^*Corresponding author for this work

School of Mathematics and Statistics

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

10 Citations (Scopus)

Abstract

For any positive integer s, a [2,2s]-factor in a graph G is a connected even factor with maximum degree at most 2s. We prove that if every induced S(K_1,2s+1) in a graph G has at least three edges in a block of degree at most 2, then ^G2 has a [2,2s]-factor. This extends the results of Hendry and Vogler [5] and Abderrezzak et al. (1991) [1].

Original language	English
Pages (from-to)	2574-2578
Number of pages	5
Journal	Discrete Mathematics
Volume	312
Issue number	17
DOIs	https://doi.org/10.1016/j.disc.2011.09.004
Publication status	Published - 6 Sept 2012

Keywords

Connected even factor
Square of a graph

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10.1016/j.disc.2011.09.004

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abstract = "For any positive integer s, a [2,2s]-factor in a graph G is a connected even factor with maximum degree at most 2s. We prove that if every induced S(K1,2s+1) in a graph G has at least three edges in a block of degree at most 2, then G2 has a [2,2s]-factor. This extends the results of Hendry and Vogler [5] and Abderrezzak et al. (1991) [1].",

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T1 - Star subdivisions and connected even factors in the square of a graph

AU - Ekstein, Jan

AU - Holub, Pemysl

AU - Kaiser, Tomáš

AU - Xiong, Liming

AU - Zhang, Shenggui

PY - 2012/9/6

Y1 - 2012/9/6

N2 - For any positive integer s, a [2,2s]-factor in a graph G is a connected even factor with maximum degree at most 2s. We prove that if every induced S(K1,2s+1) in a graph G has at least three edges in a block of degree at most 2, then G2 has a [2,2s]-factor. This extends the results of Hendry and Vogler [5] and Abderrezzak et al. (1991) [1].

AB - For any positive integer s, a [2,2s]-factor in a graph G is a connected even factor with maximum degree at most 2s. We prove that if every induced S(K1,2s+1) in a graph G has at least three edges in a block of degree at most 2, then G2 has a [2,2s]-factor. This extends the results of Hendry and Vogler [5] and Abderrezzak et al. (1991) [1].

KW - Connected even factor

KW - Square of a graph

UR - https://www.scopus.com/pages/publications/84862661331

U2 - 10.1016/j.disc.2011.09.004

DO - 10.1016/j.disc.2011.09.004

M3 - Article

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VL - 312

SP - 2574

EP - 2578

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 17

ER -

Star subdivisions and connected even factors in the square of a graph

Abstract

Keywords

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