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A Sufficient Condition for a Graph to be the Core of a Class 2 Graph

Published online by Cambridge University Press:  01 March 2000

J. K. DUGDALE  and
A. J. W. HILTON
J. K. DUGDALE
Affiliation:
Department of Mathematics, University of Reading, Whiteknights, Reading RG6 6AX, England
A. J. W. HILTON
Affiliation:
Department of Mathematics, University of Reading, Whiteknights, Reading RG6 6AX, England
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Abstract

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The core of a graph G is the subgraph GΔ induced by the vertices of maximum degree. We define the deleted core D(G) of G. We extend an earlier sufficient condition due to Hoffman [7] for a graph H to be the core of a Class 2 graph, and thereby provide a stronger sufficient condition. The new sufficient condition is in terms of D(H). We show that in some circumstances our condition is necessary; but it is not necessary in general.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 9 , Issue 2 , March 2000 , pp. 97 - 104
Copyright
2000 Cambridge University Press