文摘
Inspired by a result of Carath茅odory [脺ber den Variabilit盲tsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen, Rend. Circ. Mat. Palermo 32 (1911) 193-217], the Carath茅odory number of a convexity space is defined as the smallest integer k such that for every subset U of the ground set V and every element u in the convex hull of U, there is a subset F of U with at most k elements such that u in the convex hull of F. We study the Carath茅odory number for generalized interval convexities and for convexity spaces derived from finite graphs. We establish structural properties, bounds, and hardness results.