On Structural Parameterizations for the 2-Club Problem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F15%3A00237626" target="_blank" >RIV/68407700:21240/15:00237626 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.dam.2014.11.026" target="_blank" >http://dx.doi.org/10.1016/j.dam.2014.11.026</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.dam.2014.11.026" target="_blank" >10.1016/j.dam.2014.11.026</a>

Result language
angličtina
Original language name
On Structural Parameterizations for the 2-Club Problem
Original language description
The NP-hard textsc{$s$-Club} problem is, given an undirected graph $G=(V,E)$ and~$ell in mathbb{N}$, to decide whether there is a vertex set~$Ssubseteq V$ of size at least~$ell$ such that the induced subgraph~$G[S]$ has diameter at most two. We make progress towards a systematic classification of the complexity of textsc{$s$-Club} with respect to a hierarchy of prominent structural graph parameters. First, we present the following tight NP-hardness results: textsc{$s$-Club} is NP-hard on graphs that become bipartite by deleting one vertex, on graphs that can be covered by three cliques, and on graphs with emph{domination number} two and emph{diameter} three. Then, we consider the parameter emph{$h$-index} of the input graph. The study of this parameteris motivated by real-world instances and the fact that textsc{$s$-Club} is fixed-parameter tractable when parameterized by the larger parameter emph{maximum degree}. We present an algorithm that solves textsc{$s$-Club} in~$|V|^{f(k)}$ ti
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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