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Boros and Gurvich 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 relying on the Strong Perfect Graph Theorem.
Bibtex entry:
| AUTHOR | = | {Kir{\'a}ly, Tam{\'a}s and Pap, J{\'u}lia}, |
| TITLE | = | {A note on kernels in h-perfect graphs}, |
| NOTE | = | {{\tt egres.elte.hu}}, |
| INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
| YEAR | = | {2007}, |
| NUMBER | = | {TR-2007-03} |