$t$-Perfection in $P_5$-Free Graphs
Henning Bruhn, Elke Fuchs · SIAM Journal on Discrete Mathematics · 2017
A graph is called $t$-perfect if its stable set polytope is fully described by nonnegativity, edge, and odd-cycle constraints. We characterize $P_5$-free $t$-perfect graphs in terms of forbidden $t$-minors. Moreover, we show that $P_5$-free $t$-perfect graphs can always be colored with three colors and that they can be recognized in polynomial time.