English

On MaxCut and the Lov\'asz theta function

Combinatorics 2023-09-12 v3

Abstract

In this short note we prove a lower bound for the MaxCut of a graph in terms of the Lov\'asz theta function of its complement. We combine this with known bounds on the Lov\'asz theta function of complements of HH-free graphs to recover many known results on the MaxCut of HH-free graphs. In particular, we give a new, very short proof of a conjecture of Alon, Krivelevich and Sudakov about the MaxCut of graphs with no cycles of length rr.

Cite

@article{arxiv.2305.18252,
  title  = {On MaxCut and the Lov\'asz theta function},
  author = {Igor Balla and Oliver Janzer and Benny Sudakov},
  journal= {arXiv preprint arXiv:2305.18252},
  year   = {2023}
}

Comments

8 pages

R2 v1 2026-06-28T10:49:29.243Z