On triangle-free graphs that do not contain a subdivision of the complete graph on four vertices as an induced subgraph

Abstract

We prove a decomposition theorem for the class of triangle-free graphs that do not contain a subdivision of the complete graph on four vertices as an induced subgraph. We prove that every graph of girth at least~5 in this class is 3-colorable.

Cited by in corpus (1)

• Triangle-free graphs that do not contain an induced subdivision of $K_4$ are 3-colorable