The independence number in graphs of maximum degree three

We prove that a K-4-free graph G of order n, size in and maximum degree at most three has an independent set of cardinality at least 1/7 (4n - m - lambda - tr), where lambda 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 [C.C. Heckman, R. Thomas, A new proof of the independence ratio of triangle-free cubic graphs, Discrete Math. 233 (2001) 233-237]. (C) 2007 Elsevier B.V. All rights reserved.