On $t$-perfect triangulations of the projective plane

TL;DR

This paper characterizes $t$-perfect triangulations of the projective plane, showing they are exactly those that are perfect and lack a $K_4$ subgraph, providing a complete structural description.

Contribution

It provides a precise characterization of $t$-perfect triangulations of the projective plane, linking $t$-perfection to perfection and the absence of $K_4$.

Findings

A triangulation is $t$-perfect iff it is perfect and contains no $K_4$

Characterization of $t$-perfect triangulations in the projective plane

Complete structural description of these triangulations

Abstract

We prove that a triangulation of the projective plane is (strongly) $t$-perfect if and only if it is perfect and contains no $K_4$.