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The independence number in graphs of maximum degree three

10 years 1 months ago
The independence number in graphs of maximum degree three
We prove that a K4-free graph G of order n, size m and maximum degree at most three has an independent set of cardinality at least 1 7 (4n - m - - tr) where counts the number of components of G whose blocks are each either isomorphic to one of four specific graphs or edges between two of these four specific graphs and tr is the maximum number of vertex-disjoint triangles in G. Our result generalizes a bound due to Heckman and Thomas (A New Proof of the Independence Ratio of Triangle-Free Cubic Graphs, Discrete Math. 233 (2001), 233-237). Keywords. independence; triangle; cubic graph 1
Jochen Harant, Michael A. Henning, Dieter Rautenba
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where DM
Authors Jochen Harant, Michael A. Henning, Dieter Rautenbach, Ingo Schiermeyer
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