Proof of Chv&tal's conjecture on maximal stable sets and maximal cliques in graphs

Authors:
Xiaotie Deng;Guojun Li;Wenan Zang
Affiliations:
Department of Computer Science, City University of Hong Kong, Hong Kong, China;School of Mathematics and Systems Science, Shandong University, Jinan 250100, China and Institute of Software, Chinese Academy of Sciences, Beijing 100080, China;Department of Mathematics, The University of Hong Kong, Hong Kong, China
Venue:
Journal of Combinatorial Theory Series B
Year:
2004

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Abstract

Grillet established conditions on a partially ordered set under which each maximal antichain meets each maximal chain. Chvátal made a conjecture in terms of graphs that strengthens Grillet's theorem. The purpose of this paper is to prove this conjecture.