Edge density and independence ratio in triangle-free graphs with maximum degree three Original Research Article

A simple polynomial-time algorithm is presented which computes independent sets of guaranteed size in connected triangle-free noncubic graphs with maximum degree 3. Let n and m denote the number of vertices and edges, respectively, and let c = m/n denote the edge density where c < 3/2. The algorithm establishes new lower bounds on the independence ratio of these graphs for 1 < c < 3/2.