Lower bounds on the independence number of certain graphs of odd girth at least seven

Authors:
Anders Sune Pedersen;Dieter Rautenbach;Friedrich Regen
Affiliations:
Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark;Institut für Optimierung und Operations Research, Universität Ulm, D-89069 Ulm, Germany;Institut für Optimierung und Operations Research, Universität Ulm, D-89069 Ulm, Germany
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

Heckman and Thomas [C.C. Heckman, R. Thomas, A new proof of the independence ratio of triangle-free cubic graphs, Discrete Math. 233 (2001) 233-237] proved that every connected subcubic triangle-free graph G has an independent set of order at least (4n(G)-m(G)-1)/7 where n(G) and m(G) denote the order and size of G, respectively. We conjecture that every connected subcubic graph G of odd girth at least seven has an independent set of order at least (5n(G)-m(G)-1)/9 and verify our conjecture under some additional technical assumptions.