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Characterizations of 2-variegated graphs and of 3-variegated graphs

✍ Scribed by Vasanti N. Bhat-Nayak; S.A. Choudum; Ranjan N. Naik

Publisher: Elsevier Science
Year: 1978
Tongue: English
Weight: 586 KB
Volume: 23
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(78)90182-6

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✦ Synopsis

A graph is said to be k-variegated if its vertex set can be partiticned into k equal parts such that each vertex is adjacent to exactly one vertex from every othe,r part not co;ltaininT, it. We prove that a graph G on 2n vertices is 2-variegated if and only if there exists a bet S of n independent edges in G such that no cycle irl G contains an odd number (II edges fron: S. We also characterize 3-variegated graphs.

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