Generalizations of Grillet's theorem on maximal stable sets and maximal cliques in graphs

DOI10.1016/0012-365X(94)00019-FzbMath0831.05036WikidataQ127109373 ScholiaQ127109373MaRDI QIDQ1897443

Wenan Zang

Publication date: 12 February 1996

Published in: Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

maximal chainpartially ordered setsmaximal cliquesChvátal's conjectureordered graphsmaximal stable setsmaximal antichainBerge's conjectureGrillet's theorem

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Combinatorics of partially ordered sets (06A07) Structural characterization of families of graphs (05C75)

Related Items (15)

A characterization of claw-free CIS graphs and new results on the order of CIS graphs ⋮ On equistable, split, CIS, and related classes of graphs ⋮ Proof of Chvátal's conjecture on maximal stable sets and maximal cliques in graphs ⋮ On CIS circulants ⋮ Strong cliques in vertex‐transitive graphs ⋮ On exact blockers and anti-blockers, \(\varDelta \)-conjecture, and related problems ⋮ Unconditional reflexive polytopes ⋮ Graphs vertex-partitionable into strong cliques ⋮ Vertex-transitive CIS graphs ⋮ Not complementary connected and not CIS \(d\)-graphs form weakly monotone families ⋮ Decomposing complete edge-chromatic graphs and hypergraphs. Revisited ⋮ Proof of Ding's conjecture on maximal stable sets and maximal cliques in planar graphs ⋮ Strong cliques in diamond-free graphs ⋮ Detecting strong cliques ⋮ Strong cliques and equistability of EPT graphs

Cites Work

• \(P_ 4\)-comparability graphs
• Maximal chains and antichains

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