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A shortness exponent for r-regular r-connected graphs

✍ Scribed by Brad Jackson; T. D. Parsons

Publisher: John Wiley and Sons
Year: 1982
Tongue: English
Weight: 302 KB
Volume: 6
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190060211

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✦ Synopsis

Abstract

Let r≧ 3 be an integer. It is shown that there exists ε= ε(r), 0 < ε < 1, and an integer N = N(r) > 0 such that for all n ≧ N (if r is even) or for all even n ≧ N(if r is odd), there is an r‐connected regular graph of valency r on exactly n vertices whose longest cycles have fewer than n^ε^ vertices.

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