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

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10125750" target="_blank" >RIV/00216208:11320/12:10125750 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1007/s00453-010-9468-z" target="_blank" >http://dx.doi.org/10.1007/s00453-010-9468-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00453-010-9468-z" target="_blank" >10.1007/s00453-010-9468-z</a>

Result language

angličtina

Original language name

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

Original language 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 arbitraryfixed 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 specifiedvertices (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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2012

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Algorithmica

ISSN

0178-4617

e-ISSN

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Volume of the periodical

62

Issue of the periodical within the volume

1-2

Country of publishing house

DE - GERMANY

Number of pages

21

Pages from-to

499-519

UT code for WoS article

000298388200022

EID of the result in the Scopus database

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