Abstract
A set K of vertices in a connected graph is M-convex if and only if for every pair of vertices in K, all vertices of all chordless paths joining them also lie in K. Carathéodory, Helly and Radon type theorems are proved for M-convex sets. The Carathéodory number is 1 for complete graphs and 2 for other graphs. The Helly number equals the size of a maximum clique. The Radon number is one more than the Helly number except possibly for triangle-free graphs, where it is at most 4.
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