A Helly theorem for convexity in graphs (Q799698)
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scientific article; zbMATH DE number 3873381
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Helly theorem for convexity in graphs |
scientific article; zbMATH DE number 3873381 |
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A Helly theorem for convexity in graphs (English)
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1984
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A set K of nodes of a (finite, simple, loopless, undirected) graph G is called m-convex (geodesically convex) if for each pair x, y of nodes of K all nodes on chordless (shortest) paths joining x and y are also in K. The authors prove that for any connected G the Helly number of the m- convex sets equals the clique number of G, while an analogous result for geodesically convex sets does not hold.
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abstract convexity
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Helly number
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clique number
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geodesically convex sets
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