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Complétions d'intervalles minimales

Abstract : Pathwidth and treewidth have been introduced by Robertson and Seymour in their work on graph minors. Informally, pathwidth (resp. treewidth) measures the "distance" between a given graph and the class of paths (resp. trees). Given an arbitrary graph G=(V,E), an interval graph H=(V,F) containing G is called an interval completion of G. Computing pathwidth comes to computing an interval completion of minimum cliquesize of the input graph. Unfortunately the pathwidth problem is NP-hard. We focus on minimal interval completions of G, that is interval completions H such that no proper subgraph of H is an interval completion of G. We give several algorithms for computing minimal interval completions of an input graph, an also an algorithm computing a minimal proper interval completion. Eventually, we show that pathwidth can be polinomially computed for circular-arc graphs.
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Submitted on : Tuesday, May 4, 2010 - 7:39:15 PM
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  • HAL Id : tel-00480669, version 1


Karol Suchan. Complétions d'intervalles minimales. Computer Science [cs]. Université d'Orléans, 2006. English. ⟨tel-00480669⟩



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