On three measures of non-convexity

被引：0
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作者：
Josef Cibulka
Miroslav Korbelář
Jan Kynčl
Viola Mészáros
Rudolf Stolař
Pavel Valtr
机构：
[1] Charles University,Department of Applied Mathematics and Institute for Theoretical Computer Science
[2] Faculty of Mathematics and Physics,Department of Mathematics and Statistics, Faculty of Science
[3] Masaryk University,University of Szeged
[4] Bolyai Institute,undefined
来源：
Israel Journal of Mathematics | 2017年 / 218卷
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摘要：
The invisibility graph I(X) of a set X ⊆ Rd is a (possibly infinite) graph whose vertices are the points of X and two vertices are connected by an edge if and only if the straight-line segment connecting the two corresponding points is not fully contained in X. We consider the following three parameters of a set X: the clique number ω(I(X)), the chromatic number χ(I(X)) and the convexity number γ(X), which is the minimum number of convex subsets of X that cover X.
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页码：331 / 369
页数：38
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