On treewidth and minimum fill-in of asteroidal triple-free graphs
نویسندگان
چکیده
منابع مشابه
On Treewidth and Minimum Fill-In of Asteroidal Triple-Free Graphs
We present O(n’R + n3R3) time algorithms to compute the treewidth, pathwidth, minimum fill-in and minimum interval graph completion of asteroidal triple-free graphs, where n is the number of vertices and R is the number of minimal separators of the input graph. This yields polynomial time algorithms for the four NP-complete graph problems on any subclass of the asteroidal triple-free graphs tha...
متن کاملAsteroidal Triple-Free Graphs
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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We show that the minimum fill-in and the minimum interval graph completion of a d-trapezoid graph can be computed in time O(n). We also show that the treewidth and the pathwidth of a d-trapezoid graph can be computed by an O(n tw(G) ) time algorithm. For both algorithms, d is supposed to be a fixed positive integer and it is required that a suitable intersection model of the given d-trapezoid g...
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We introduce the notion of potential maximal cliquee of a graph and we use it for computing the treewidth and the minimum ll-in of graphs for which the the potential maximal cliques can be listed in polynomial time. Finally we show how to compute the potential maximal cliques of weakly triangulated graphs. triangulations RRsumm Nous introduisons la notion de clique potentielle maximalee d'un gr...
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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: Theoretical Computer Science
سال: 1997
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(96)00206-x