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Description
  • We answer in the negative a question of Oporowski and Zhao [Discrete Math., 309 (2009), pp. 2948-2951] asking whether every graph with crossing number at most 5 and clique number at most 5 is 5-colorable. However, we show that every graph with crossing number at most 4 and clique number at most 5 is 5-colorable. We also show some colorability results on graphs that can be made planar by removing a few edges. In particular, we show that, if a graph with clique number at most 5 has three edges whose removal leaves the graph planar, then it is 5-colorable.
  • We answer in the negative a question of Oporowski and Zhao [Discrete Math., 309 (2009), pp. 2948-2951] asking whether every graph with crossing number at most 5 and clique number at most 5 is 5-colorable. However, we show that every graph with crossing number at most 4 and clique number at most 5 is 5-colorable. We also show some colorability results on graphs that can be made planar by removing a few edges. In particular, we show that, if a graph with clique number at most 5 has three edges whose removal leaves the graph planar, then it is 5-colorable. (en)
Title
  • 5-Coloring Graphs with 4 Crossings
  • 5-Coloring Graphs with 4 Crossings (en)
skos:prefLabel
  • 5-Coloring Graphs with 4 Crossings
  • 5-Coloring Graphs with 4 Crossings (en)
skos:notation
  • RIV/00216208:11320/11:10102938!RIV12-GA0-11320___
http://linked.open...avai/predkladatel
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/09/0197), Z(MSM0021620838)
http://linked.open...iv/cisloPeriodika
  • 25
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 244200
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/11:10102938
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • girth; clique number; crossing number; chromatic number (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [10E7E4DDB118]
http://linked.open...i/riv/nazevZdroje
  • SIAM Journal on Discrete Mathematics
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 2011
http://linked.open...iv/tvurceVysledku
  • Lidický, Bernard
  • Havet, Frédéric
  • Erman, Rok
  • Pangrác, Ondřej
http://linked.open...ain/vavai/riv/wos
  • 000288983400022
http://linked.open...n/vavai/riv/zamer
issn
  • 0895-4801
number of pages
http://bibframe.org/vocab/doi
  • 10.1137/100784059
http://localhost/t...ganizacniJednotka
  • 11320
is http://linked.open...avai/riv/vysledek of
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