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arXiv · 2412.17735

Colouring t-perfect graphs

Maria Chudnovsky·Linda Cook·James Davies·Sang-il Oum·Jane Tan
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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.

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Maria Chudnovsky, Linda Cook, James Davies, Sang-il Oum, Jane Tan. 2024-12-23. Colouring t-perfect graphs. https://arxiv.org/abs/2412.17735

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