A Helly theorem for convexity in graphs
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.
scientific article; zbMATH DE number 3873381
scientific article