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  • 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. (en)
Title
  • Beyond homothetic polygons: recognition and maximum clique
  • Beyond homothetic polygons: recognition and maximum clique (en)
skos:prefLabel
  • Beyond homothetic polygons: recognition and maximum clique
  • Beyond homothetic polygons: recognition and maximum clique (en)
skos:notation
  • RIV/00216208:11320/12:10128144!RIV13-GA0-11320___
http://linked.open...avai/riv/aktivita
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  • P(GEGIG/11/E023)
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  • 7676
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  • 124792
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  • RIV/00216208:11320/12:10128144
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  • maximum clique; recognition problem; complexity; homothetic convex polygons (en)
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  • DE - Spolková republika Německo
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  • [B5A4F05F5DD3]
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  • Lecture Notes in Computer Science
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  • 7676
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  • Kratochvíl, Jan
  • Junosza-Szaniawski, Konstanty
  • Pergel, Martin
  • Rzążewski, Paweł
issn
  • 0302-9743
number of pages
http://bibframe.org/vocab/doi
  • 10.1007/978-3-642-35261-4_64
http://localhost/t...ganizacniJednotka
  • 11320
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