Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Collapsible graphs and reductions of line graphs

Language

English

Abstract

A graph G is collapsible if for every even subset X ⊆ V (G), G has a subgraph Γ such that G - E (Γ) is connected and the set of odd-degree vertices of Γ is X. A graph obtained by contracting all the non-trivial collapsible subgraphs of G is called the reduction of G. In this paper, we characterize graphs of diameter two in terms of collapsible subgraphs and investigate the relationship between the line graph of the reduction and the reduction of the line graph. Our results extend former results in [H.-J. Lai, Reduced graph of diameter two, J. Graph Theory 14 (1) (1990) 77-87], and in [P.A. Catlin, Iqblunnisa, T.N. Janakiraman, N. Srinivasan, Hamilton cycles and closed trails in iterated line graphs, J. Graph Theory 14 (1990) 347-364]. © 2008 Elsevier B.V. All rights reserved.

Keywords

Collapsible graph, Double cycle covers, Hamiltonian index, Line graphs, Reduction of graph

Publication Date

2009

Source Publication Title

Discrete Mathematics

Volume

309

Issue

10

Start Page

3173

End Page

3184

Publisher

Elsevier

DOI

10.1016/j.disc.2008.09.014

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.disc.2008.09.014

ISSN (print)

0012365X

ISSN (electronic)

1872681X

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