Note: A note on kernels and Sperner's Lemma

Authors:
Tamás Király;Júlia Pap
Affiliations:
MTA-ELTE Egerváry Research Group, Department of Operations Research, Eötvös University, Budapest, Hungary;MTA-ELTE Egerváry Research Group, Department of Operations Research, Eötvös University, Budapest, Hungary
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

The kernel-solvability of perfect graphs was first proved by Boros and Gurvich, and later Aharoni and Holzman gave a shorter proof. Both proofs were based on Scarf's Lemma. In this note we show that a very simple proof can be given using a polyhedral version of Sperner's Lemma. In addition, we extend the Boros-Gurvich theorem to h-perfect graphs and to a more general setting.