Intersection Theorems for Infinite Families of Convex Sets in Graphs |
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Authors: | Polat Norbert |
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Affiliation: | (1) I.A.E., Université Jean Moulin, 15, Quai Claude Bernard, 69239 Lyon Cedex 2, France |
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Abstract: | We prove several Helly-type theorems for infinite families of geodesically convex sets in infinite graphs. That is, we determine the least cardinal n such that any family of (particular) convex sets in some infinite graph has a nonempty intersection whenever each of its subfamilies of cardinality less than n has a nonempty intersection. We obtain some general compactness theorems, and some particular results for pseudo-modular graphs, strongly dismantlable graphs and ball-Helly graphs. |
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Keywords: | Infinite graph geodesic convexity Helly number |
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