Colouring t-perfect graphs

TL;DR

This paper establishes a finite upper bound of 199053 on the chromatic number of t-perfect graphs, providing a key insight into their coloring properties and answering a long-standing open question.

Contribution

It proves the first finite bound on the chromatic number of t-perfect graphs, advancing understanding of their structural and coloring properties.

Findings

t-perfect graphs are 199053-colorable

Every h-perfect graph with clique number ω is (ω + 199050)-colorable

First finite bound on t-perfect graph chromatic number

Abstract

Perfect graphs can be described as the graphs whose stable set polytopes are defined by their non-negativity and clique inequalities (including edge inequalities). In 1975, Chv\'{a}tal defined an analogous class of t-perfect graphs, which are the graphs whose stable set polytopes are defined by their non-negativity, edge inequalities, and odd circuit inequalities. We show that t-perfect graphs are $199053$-colourable. This is the first finite bound on the chromatic number of t-perfect graphs and answers a question of Shepherd from 1995. Our proof also shows that every h-perfect graph with clique number $\omega$ is $(\omega + 199050)$-colourable.