Boxicity and cubicity of asteroidal triple free graphs
نویسندگان
چکیده
منابع مشابه
Boxicity and cubicity of asteroidal triple free graphs
An axis parallel d-dimensional box is the Cartesian product R1×R2×· · ·×Rd where each Ri is a closed interval on the real line. The boxicity of a graph G, denoted as box(G), is the minimum integer d such that G can be represented as the intersection graph of a collection of d-dimensional boxes. An axis parallel unit cube in d-dimensional space or a d-cube is defined as the Cartesian product R1 ...
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An independent set of three vertices such that each pair is joined by a path that avoids the neighborhood of the third is called an asteroidal triple. A graph is asteroidal triple-free (AT-free) if it contains no asteroidal triples. The motivation for this investigation was provided, in part, by the fact that the AT-free graphs provide a common generalization of interval, permutation, trapezoid...
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In this paper, we study the metric property of LexBFS-ordering on AT-free graphs. Based on a 2-sweep LexBFS algorithm, we show that every AT-free graph admits a vertex ordering, called the strong 2-cocomparability ordering, that for any three vertices u v w in the ordering, if d(u; w) 2 then d(u; v) = 1 or d(v; w) 2. As an application of this ordering, we provide a simple linear time recognitio...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2010.01.020