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Description
  • Interval graphs are intersection graphs of closed intervals. A generalization of recognition called partial representation extension was introduced recently. The input gives an interval graph with a partial representation specifying some pre-drawn intervals. We ask whether the remaining intervals can be added to create an extending representation. In this paper, we characterize the minimal obstructions which make a partial representation non-extendible. This generalizes Lekkerkerker and Boland's characterization of minimal forbidden induced subgraphs of interval graphs. Each minimal obstruction consists of a forbidden induced subgraph together with at most four pre-drawn intervals. A Helly-type result follows: A partial representation is extendible if and only if every quadruple of pre-drawn intervals is extendible by itself. Our characterization leads to the first polynomial-time certifying algorithm for partial representation extension of intersection graphs.
  • Interval graphs are intersection graphs of closed intervals. A generalization of recognition called partial representation extension was introduced recently. The input gives an interval graph with a partial representation specifying some pre-drawn intervals. We ask whether the remaining intervals can be added to create an extending representation. In this paper, we characterize the minimal obstructions which make a partial representation non-extendible. This generalizes Lekkerkerker and Boland's characterization of minimal forbidden induced subgraphs of interval graphs. Each minimal obstruction consists of a forbidden induced subgraph together with at most four pre-drawn intervals. A Helly-type result follows: A partial representation is extendible if and only if every quadruple of pre-drawn intervals is extendible by itself. Our characterization leads to the first polynomial-time certifying algorithm for partial representation extension of intersection graphs. (en)
Title
  • Minimal Obstructions for Partial Representations of Interval Graphs
  • Minimal Obstructions for Partial Representations of Interval Graphs (en)
skos:prefLabel
  • Minimal Obstructions for Partial Representations of Interval Graphs
  • Minimal Obstructions for Partial Representations of Interval Graphs (en)
skos:notation
  • RIV/00216208:11320/14:10288454!RIV15-MSM-11320___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GBP202/12/G061), S
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
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  • 29461
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  • RIV/00216208:11320/14:10288454
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  • minimal obstruction; partial representation; interval graph (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [EBA7E2ED7F1F]
http://linked.open...v/mistoKonaniAkce
  • Jeonju, South Korea
http://linked.open...i/riv/mistoVydani
  • Switzerland
http://linked.open...i/riv/nazevZdroje
  • Algorithms and Computation
http://linked.open...in/vavai/riv/obor
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http://linked.open...vavai/riv/projekt
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  • Klavík, Pavel
  • Saumell, Maria
http://linked.open...vavai/riv/typAkce
http://linked.open.../riv/zahajeniAkce
issn
  • 0302-9743
number of pages
http://bibframe.org/vocab/doi
  • 10.1007/978-3-319-13075-0_32
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  • Springer International Publishing
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  • 978-3-319-13074-3
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  • 11320
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