About: The k-in-a-Path Problem for Claw-free Graphs

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.1007/s00453-010-9468-z
Description	The k-in-a-Path problem is to test whether a graph contains an induced path spanning k given vertices. This problem is NP-complete in general graphs, already when k=3. We show how to solve it in polynomial time on claw-free graphs, when k is an arbitrary fixed integer not part of the input. As a consequence, also the k-Induced Disjoint Paths and the k-in-a-Cycle problem are solvable in polynomial time on claw-free graphs for any fixed k. The first problem has as input a graph G and k pairs of specified vertices (s (i) ,t (i) ) for i=1,aEuro broken vertical bar,k and is to test whether G contain k mutually induced paths P (i) such that P (i) connects s (i) and t (i) for i=1,aEuro broken vertical bar,k. The second problem is to test whether a graph contains an induced cycle spanning k given vertices. When k is part of the input, we show that all three problems are NP-complete, even for the class of line graphs, which form a subclass of the class of claw-free graphs. The k-in-a-Path problem is to test whether a graph contains an induced path spanning k given vertices. This problem is NP-complete in general graphs, already when k=3. We show how to solve it in polynomial time on claw-free graphs, when k is an arbitrary fixed integer not part of the input. As a consequence, also the k-Induced Disjoint Paths and the k-in-a-Cycle problem are solvable in polynomial time on claw-free graphs for any fixed k. The first problem has as input a graph G and k pairs of specified vertices (s (i) ,t (i) ) for i=1,aEuro broken vertical bar,k and is to test whether G contain k mutually induced paths P (i) such that P (i) connects s (i) and t (i) for i=1,aEuro broken vertical bar,k. The second problem is to test whether a graph contains an induced cycle spanning k given vertices. When k is part of the input, we show that all three problems are NP-complete, even for the class of line graphs, which form a subclass of the class of claw-free graphs. (en)
Title	The k-in-a-Path Problem for Claw-free Graphs The k-in-a-Path Problem for Claw-free Graphs (en)
skos:prefLabel	The k-in-a-Path Problem for Claw-free Graphs The k-in-a-Path Problem for Claw-free Graphs (en)
skos:notation	RIV/00216208:11320/12:10125750!RIV13-GA0-11320___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(1M0545), P(GA201/09/0197)
http://linked.open...iv/cisloPeriodika	1-2
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Lidický, Bernard Fiala, Jiří
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	144625
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/12:10125750
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Polynomial time algorithm; Claw-free graph; Induced path (en)
http://linked.open.../riv/klicoveSlovo	Induced path Polynomial time algorithm Claw-free graph
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[65428F58847F]
http://linked.open...i/riv/nazevZdroje	Algorithmica
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...vavai/riv/projekt	Institute for Theoretical Computer Science Graph colorings and flows: structure and applications
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	62
http://linked.open...iv/tvurceVysledku	Fiala, Jiří Lidický, Bernard Kaminski, Marcin Paulusma, Daniel
http://linked.open...ain/vavai/riv/wos	000298388200022
issn	0178-4617
number of pages	21 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s00453-010-9468-z
http://localhost/t...ganizacniJednotka	11320

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