Lower Bounds for Max-Cut in $H$-Free Graphs via Semidefinite Programming

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