Convexity in Graphs and Hypergraphs
Martin Farber, Robert E. Jamison · SIAM Journal on Algebraic and Discrete Methods · 1986
We study several notions of abstract convexity in graphs and hypergraphs. In each case, we obtain analogues of several classical results, including the Minkowski–Krein–Milman theorem, Caratheodory’s theorem and Tietze’s convexity theorem. In addition, our results yield new characterizations of the classes of chordal gaphs, strongly chordal graphs, Ptolemaic graphs and totally balanced hypergraphs.