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On the theta number of powers of cycle graphs

✍ Scribed by Christine Bachoc, Arnaud Pêcher, Alain Thiéry

Book ID
120912589
Publisher
Springer-Verlag
Year
2013
Tongue
English
Weight
241 KB
Volume
33
Category
Article
ISSN
0209-9683

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## Abstract Let __G__ be a graph on __p__ vertices with __q__ edges and let __r__ = __q__ − __p__ = 1. We show that __G__ has at most ${15\over 16} 2^{r}$ cycles. We also show that if __G__ is planar, then __G__ has at most 2^__r__ − 1^ = __o__(2^__r__ − 1^) cycles. The planar result is best possib