Ensemble convexes dans les graphes. I: Théoremes de Helly et de Radon pour graphes et surfaces

DOI10.1016/S0195-6698(83)80041-9zbMath0523.05031OpenAlexW165014760MaRDI QIDQ1056760

Henri Meyniel, Pierre Duchet

Publication date: 1983

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0195-6698(83)80041-9

zbMATH Keywords

contractionHadwiger numberchromatic number of the surface

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Helly-type theorems and geometric transversal theory (52A35)

Related Items (14)

On local convexity in graphs ⋮ Convexity in Graphs and Hypergraphs ⋮ 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 ⋮ Star-shape, Radon number, and minty graphs ⋮ Tverberg numbers for cellular bipartite graphs ⋮ The colorful Helly theorem and general hypergraphs ⋮ Graphs with convex balls ⋮ Turán theorems and convexity invariants for directed graphs ⋮ Graphs with intrinsic s3 convexities ⋮ Unnamed Item ⋮ Graph theory (algorithmic, algebraic, and metric problems) ⋮ A Helly theorem for convexity in graphs

Cites Work

• Every planar map is four colorable. I: Discharging
• Über eine Übertragung des Hellyschen Satzes in Sphärische Räume
• The embeddings of a graph—A survey
• Toward a theory of crossing numbers
• Some Elementary Properties of Interval Convexities
• Some generalizations of Helly’s theorem on convex sets
• Two Consequences of the Transposition Theorem on Linear Inequalities
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