The chromatic number of heptagraphs

Abstract

A pentagraph is a graph without cycles of length 3 or 4 and without induced cycles of odd length at least 7, and a heptagraph is one without cycles of length less than 7 and without induced cycles of odd length at least 9. Chudnovsky and Seymour proved that every pentagraph is 3-colorable. In this paper, we show that every heptagraph is 3-colorable.