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On graphs with equal edge-connectivity and minimum degree

✍ Scribed by Donald L. Goldsmith; Arthur T. White

Publisher: Elsevier Science
Year: 1978
Tongue: English
Weight: 599 KB
Volume: 23
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(78)90184-x

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✦ Synopsis

It was proved by Chartrand f hat if G is a graph of order p for which the minimum degree is at least [&I, then the edge-connectivity of G equals the minimum degree of G. It is shown here that one may allow vertices of degree less than $p and still obtain the same conclusion, provided the degrees are essentially "balanced"; that is, for each vertex with degree less th;i; $p there is an associated vertex with degree sufficiently greater than $p.

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