$t$-perfection in $P_5$-free graphs

TL;DR

This paper characterizes $P_5$-free $t$-perfect graphs using forbidden $t$-minors, proves they are 3-colorable, and provides a polynomial-time recognition algorithm.

Contribution

It offers a forbidden $t$-minor characterization for $P_5$-free $t$-perfect graphs and establishes their 3-colorability and polynomial recognition.

Findings

Characterization of $P_5$-free $t$-perfect graphs via forbidden $t$-minors

Proof that these graphs are 3-colorable

Development of a polynomial-time recognition algorithm

Abstract

A graph is called $t$-perfect if its stable set polytope is fully described by non-negativity, edge and odd-cycle constraints. We characterise $P_5$-free $t$-perfect graphs in terms of forbidden $t$-minors. Moreover, we show that $P_5$-free $t$-perfect graphs can always be coloured with three colours, and that they can be recognised in polynomial time.