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On the Number of Cycles in 3-Connected Cubic Graphs

✍ Scribed by R.E.L Aldred; Carsten Thomassen

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 228 KB
Volume: 71
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.1997.1771

No coin nor oath required. For personal study only.

✦ Synopsis

Let f (n) be the minimum number of cycles present in a 3-connected cubic graph on n vertices. In 1986, C. A. Barefoot, L. Clark, and R. Entringer (Congr. Numer. 53, 1986) showed that f (n) is subexponential and conjectured that f (n) is superpolynomial. We verify this by showing that, for n sufficiently large, 2 n 0.17 < f(n) 2 n 0.95 .

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