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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F12%3A10128144%21RIV13-GA0-11320___
rdf:type
n6:Vysledek skos:Concept
dcterms: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. 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.
dcterms:title
Beyond homothetic polygons: recognition and maximum clique Beyond homothetic polygons: recognition and maximum clique
skos:prefLabel
Beyond homothetic polygons: recognition and maximum clique Beyond homothetic polygons: recognition and maximum clique
skos:notation
RIV/00216208:11320/12:10128144!RIV13-GA0-11320___
n6:predkladatel
n15:orjk%3A11320
n3:aktivita
n10:P
n3:aktivity
P(GEGIG/11/E023)
n3:cisloPeriodika
7676
n3:dodaniDat
n4:2013
n3:domaciTvurceVysledku
n12:4476468 n12:1123580
n3:druhVysledku
n20:J
n3:duvernostUdaju
n19:S
n3:entitaPredkladatele
n14:predkladatel
n3:idSjednocenehoVysledku
124792
n3:idVysledku
RIV/00216208:11320/12:10128144
n3:jazykVysledku
n13:eng
n3:klicovaSlova
maximum clique; recognition problem; complexity; homothetic convex polygons
n3:klicoveSlovo
n7:recognition%20problem n7:homothetic%20convex%20polygons n7:maximum%20clique n7:complexity
n3:kodStatuVydavatele
DE - Spolková republika Německo
n3:kontrolniKodProRIV
[B5A4F05F5DD3]
n3:nazevZdroje
Lecture Notes in Computer Science
n3:obor
n9:IN
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
4
n3:projekt
n18:GEGIG%2F11%2FE023
n3:rokUplatneniVysledku
n4:2012
n3:svazekPeriodika
7676
n3:tvurceVysledku
Pergel, Martin Rzążewski, Paweł Junosza-Szaniawski, Konstanty Kratochvíl, Jan
s:issn
0302-9743
s:numberOfPages
10
n5:doi
10.1007/978-3-642-35261-4_64
n16:organizacniJednotka
11320