Cycles passing through k + 1 vertices in k-connected graphs

Jun Fujisawa; Tomoki Yamashita

doi:10.1002/jgt.20306

Cycles passing through k + 1 vertices in k-connected graphs

Jun Fujisawa, Tomoki Yamashita

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

2 Citations (Scopus)

Abstract

In this article, we prove the following theorem. Let k ≥ 3 be an integer, G be a k-connected graph with minimum degree d and X be a set of k+ 1 vertices on a cycle. Then G has a cycle of length at least min{2d, | V(G)|} passing through X. This result gives the positive answer to the Question posed by Locke [8].

Original language	English
Pages (from-to)	179-190
Number of pages	12
Journal	Journal of Graph Theory
Volume	58
Issue number	2
DOIs	https://doi.org/10.1002/jgt.20306
Publication status	Published - 2008 Jun
Externally published	Yes

Keywords

Cyclable
Long cycle
Minimum degree

ASJC Scopus subject areas

Geometry and Topology

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10.1002/jgt.20306

Cite this

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abstract = "In this article, we prove the following theorem. Let k ≥ 3 be an integer, G be a k-connected graph with minimum degree d and X be a set of k+ 1 vertices on a cycle. Then G has a cycle of length at least min{2d, | V(G)|} passing through X. This result gives the positive answer to the Question posed by Locke [8].",

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AB - In this article, we prove the following theorem. Let k ≥ 3 be an integer, G be a k-connected graph with minimum degree d and X be a set of k+ 1 vertices on a cycle. Then G has a cycle of length at least min{2d, | V(G)|} passing through X. This result gives the positive answer to the Question posed by Locke [8].

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KW - Long cycle

KW - Minimum degree

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Cycles passing through k + 1 vertices in k-connected graphs

Abstract

Keywords

ASJC Scopus subject areas

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