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A sufficient condition for a regular graph to be class 1

✍ Scribed by A. J. W. Hilton; Cheng Zhao

Publisher: John Wiley and Sons
Year: 1993
Tongue: English
Weight: 553 KB
Volume: 17
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190170607

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✦ Synopsis

Abstract

The core __G__Δ of a simple graph G is the subgraph induced by the vertices of maximum degree. It is well known that the Petersen graph is not 1‐factorizable and has property that the core of the graph obtained from it by removing one vertex has maximum degree 2. In this paper, we prove the following result. Let G be a regular graph of even order with d(G) ≥ 3. Suppose that G contains a vertex ν such that the core of G\ν has maximum degree 2. If G is not the Petersen graph, then G is 1‐factorizable. © 1993 John Wiley & Sons, Inc.

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