Boros and Gurvich [3] showed that every clique-acyclic superorientation of a perfect graph has a kernel. We prove the following extension of their result: if G is an h-perfect graph, then every clique-acyclic and odd-hole-acyclic superorientation of G has a kernel. We propose a conjecture related to Scarf’s Lemma that would imply the reverse direction of the Boros-Gurvich theorem without relyin...
In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and the icosahedral graph.
