Bipartite graphs decomposable into closed trails

Sylwia Cichacz; Dalibar Froncek

Bipartite graphs decomposable into closed trails

Sylwia Cichacz
, Dalibar Froncek

Mathematics & Statistics

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

Abstract

Let G = K_a,b, where a, b are even or G = K_a,a -M _2a,, where a > 1 is an odd integer and M_2a is a perfect matching in K_a,a. It has been shown ([3,4]) that G is arbitrarily decomposable into closed trails. Billington asked if the graph K_r,s, -F, where s,r are odd and F is a (smallest possible) spanning subgraph of odd degree, is arbitrarily decomposable into closed trails ([2]). In this article we answer the question in the affirmative.

Original language	English (US)
Pages (from-to)	207-216
Number of pages	10
Journal	Journal of Combinatorial Mathematics and Combinatorial Computing
Volume	74
State	Published - Aug 1 2010

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title = "Bipartite graphs decomposable into closed trails",

abstract = "Let G = Ka,b, where a, b are even or G = Ka,a -M 2a,, where a > 1 is an odd integer and M2a is a perfect matching in Ka,a. It has been shown ([3,4]) that G is arbitrarily decomposable into closed trails. Billington asked if the graph Kr,s, -F, where s,r are odd and F is a (smallest possible) spanning subgraph of odd degree, is arbitrarily decomposable into closed trails ([2]). In this article we answer the question in the affirmative.",

author = "Sylwia Cichacz and Dalibar Froncek",

year = "2010",

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language = "English (US)",

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journal = "Journal of Combinatorial Mathematics and Combinatorial Computing",

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N2 - Let G = Ka,b, where a, b are even or G = Ka,a -M 2a,, where a > 1 is an odd integer and M2a is a perfect matching in Ka,a. It has been shown ([3,4]) that G is arbitrarily decomposable into closed trails. Billington asked if the graph Kr,s, -F, where s,r are odd and F is a (smallest possible) spanning subgraph of odd degree, is arbitrarily decomposable into closed trails ([2]). In this article we answer the question in the affirmative.

AB - Let G = Ka,b, where a, b are even or G = Ka,a -M 2a,, where a > 1 is an odd integer and M2a is a perfect matching in Ka,a. It has been shown ([3,4]) that G is arbitrarily decomposable into closed trails. Billington asked if the graph Kr,s, -F, where s,r are odd and F is a (smallest possible) spanning subgraph of odd degree, is arbitrarily decomposable into closed trails ([2]). In this article we answer the question in the affirmative.

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M3 - Article

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JO - Journal of Combinatorial Mathematics and Combinatorial Computing

JF - Journal of Combinatorial Mathematics and Combinatorial Computing

ER -

Bipartite graphs decomposable into closed trails

Abstract

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