Lower bounds for max-cut in h-free graphs via semidefinite programming

For a graph G, let f(G) denote the size of the maximum cut in G. The problem of estimating f(G) as a function of the number of vertices and edges of G has a long history and was extensively studied in the last fifty years. In this paper we propose an approach, based on semidefinite programming, to prove lower bounds on f(G). We use this approach to find large cuts in graphs with few triangles and in Kr-free graphs.