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Degree sums for edges and cycle lengths in graphs

✍ Scribed by Brandt, Stephan; Veldman, Henk Jan

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 71 KB
Volume: 25
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199708)25:4<253::aid-jgt2>3.0.co;2-j

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✦ Synopsis

Let G be a graph of order n satisfying d(u) + d(v) ≥ n for every edge uv of G. We show that the circumference-the length of a longest cycle-of G can be expressed in terms of a certain graph parameter, and can be computed in polynomial time. Moreover, we show that G contains cycles of every length between 3 and the circumference, unless G is complete bipartite. If G is 1-tough then it is pancyclic or G = K r,r with r = n/2.

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