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 (SDP), to prove lower bounds on $f(G)$. We use this approach to find large cuts in graphs with few triangles and in $K_r$-free graphs.
- Pub Date:
- October 2018
- Computer Science - Data Structures and Algorithms;
- Mathematics - Combinatorics
- 21 pages, to be published in LATIN 2020 proceedings, Updated version is rewritten to include additional results along with corrections to original arguments