Parameterized Complexity of Generalized Domination Problems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F10%3A10057006" target="_blank" >RIV/00216208:11320/10:10057006 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Parameterized Complexity of Generalized Domination Problems
Original language description
Given two sets sigma, ró of nonnegative integers, a set S of vertices of a graph G is (sigma,ró)-dominating if |S ? N(v)| ? sigma for every vertex v ? S, and |S ? N(v)| ? ró for every v ? S. This concept, introduced by Telle in 1990's, generalizes and unifies several variants of graph domination studied separately before. We study the parameterized complexity of (sigma,ró)-domination in this general setting. Among other results we show that existence of a (sigma,ró)-dominating set of size k (and at mostk) are W[1]-complete problems (when parameterized by k) for any pair of finite sets sigma and ró. We further present results on dual parametrization by n ? k, and results on certain infinite sets (in particular for sigma, ró being the sets of even and odd integers).
Czech name
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Czech description
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Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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