Convexity in graphs and hypergraphs
Convexity in graphs and hypergraphs
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DOI：
10.1137/0607049
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发表时间：
1986-07
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影响因子：
--
通讯作者：
M. Farber;R. Jamison
中科院分区：
文献类型：
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作者：
M. Farber;R. Jamison
本文研究了图和超图的抽象凸性的几个概念。在每种情况下，我们得到类似的几个经典的结果，包括Minkowski-Krein-Milman定理，Caratheodory定理和Tietze的凸性定理。此外，我们的结果还给出了弦间隙、强弦图、托勒密图和完全平衡超图类的新刻画。
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.