A Helly theorem for convexity in graphs

DOI10.1016/0012-365X(84)90021-9zbMath0548.05052OpenAlexW2063849229MaRDI QIDQ799698

Robert E. Jamison, Richard J. Nowakowski

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1016/0012-365x(84)90021-9

zbMATH Keywords

clique numberabstract convexityHelly numbergeodesically convex sets

Mathematics Subject Classification ID

Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Graph theory (05C99) Helly-type theorems and geometric transversal theory (52A35)

Related Items (14)

Complexity aspects of the triangle path convexity ⋮ On local convexity in graphs ⋮ A Helly theorem for geodesic convexity in strongly dismantlable graphs ⋮ Convex sets in graphs. II: Minimal path convexity ⋮ A Helly theorem in weakly modular space ⋮ Inapproximability results and bounds for the Helly and Radon numbers of a graph ⋮ Centers of triangulated graphs ⋮ Some properties of graph centroids ⋮ Turán theorems and convexity invariants for directed graphs ⋮ Helly theorems for 3-Steiner and 3-monophonic convexity in graphs ⋮ Complexity results related to monophonic convexity ⋮ Graph theory (algorithmic, algebraic, and metric problems) ⋮ On the minimum sum coloring of \(P_4\)-sparse graphs ⋮ A one-to-one correspondence between potential solutions of the cluster deletion problem and the minimum sum coloring problem, and its application to \(P_4\)-sparse graphs

Cites Work

• Some aspects of perfect elimination orderings in chordal graphs
• Ensemble convexes dans les graphes. I: Théoremes de Helly et de Radon pour graphes et surfaces
• Partition numbers for trees and ordered sets
• The edge inducibility of graphs
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