Beyond homothetic polygons: recognition and maximum clique
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10128144" target="_blank" >RIV/00216208:11320/12:10128144 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-642-35261-4_64" target="_blank" >http://dx.doi.org/10.1007/978-3-642-35261-4_64</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-642-35261-4_64" target="_blank" >10.1007/978-3-642-35261-4_64</a>
Alternative languages
Result language
angličtina
Original language name
Beyond homothetic polygons: recognition and maximum clique
Original language description
We study the Clique problem in classes of intersection graphs of convex sets in the plane. The problem is known to be NP-complete in convex-sets intersection graphs and straight-line-segments intersection graphs, but solvable in polynomial time in intersection graphs of homothetic triangles. We extend the latter result by showing that for every convex polygon P with k sides, every n-vertex graph which is an intersection graph of homothetic copies of P contains at most n 2k inclusion-wise maximal cliques. We actually prove this result for a more general class of graphs, so called k DIR -CONV, which are intersection graphs of convex polygons whose all sides are parallel to at most k directions. We further provide lower bounds on the numbers of maximal cliques, discuss the complexity of recognizing these classes of graphs and present relationship with other classes of convex-sets intersection graphs.
Czech name
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Czech description
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Classification
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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Result continuities
Project
<a href="/en/project/GEGIG%2F11%2FE023" target="_blank" >GEGIG/11/E023: Graph Drawings and Representations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Lecture Notes in Computer Science
ISSN
0302-9743
e-ISSN
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Volume of the periodical
7676
Issue of the periodical within the volume
7676
Country of publishing house
DE - GERMANY
Number of pages
10
Pages from-to
619-628
UT code for WoS article
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EID of the result in the Scopus database
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