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Description
  • A colouring of the vertices of a graph is called injective if every two distinct vertices connected by a path of length 2 receive different colours, and it is called locally injective if it is an injective proper colouring. We show that for k }= 4, deciding the existence of a locally injective k-colouring, and of an injective k-colouring, are NP-complete problems even when restricted to planar graphs. It is known that every planar graph of maximum degree {= 3/5k - 52 allows a locally injective k-colouring. To compare the behaviour of planar and general graphs we show that for general graphs, deciding the existence of a locally injective k-colouring becomes NP-complete for graphs of maximum degree 2 root k (when k }= 7).
  • A colouring of the vertices of a graph is called injective if every two distinct vertices connected by a path of length 2 receive different colours, and it is called locally injective if it is an injective proper colouring. We show that for k }= 4, deciding the existence of a locally injective k-colouring, and of an injective k-colouring, are NP-complete problems even when restricted to planar graphs. It is known that every planar graph of maximum degree {= 3/5k - 52 allows a locally injective k-colouring. To compare the behaviour of planar and general graphs we show that for general graphs, deciding the existence of a locally injective k-colouring becomes NP-complete for graphs of maximum degree 2 root k (when k }= 7). (en)
Title
  • Locally injective k-colourings of planar graphs
  • Locally injective k-colourings of planar graphs (en)
skos:prefLabel
  • Locally injective k-colourings of planar graphs
  • Locally injective k-colourings of planar graphs (en)
skos:notation
  • RIV/00216208:11320/14:10282425!RIV15-GA0-11320___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GBP202/12/G061)
http://linked.open...iv/cisloPeriodika
  • August
http://linked.open...vai/riv/dodaniDat
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  • 26488
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/14:10282425
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  • Complexity; Planar graph; Graph colouring; Locally injective colouring (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • NL - Nizozemsko
http://linked.open...ontrolniKodProRIV
  • [E54CFC8FCF11]
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  • Discrete Applied Mathematics
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http://linked.open...v/svazekPeriodika
  • 173
http://linked.open...iv/tvurceVysledku
  • Kratochvíl, Jan
  • Siggers, Mark
http://linked.open...ain/vavai/riv/wos
  • 000337204100007
issn
  • 0166-218X
number of pages
http://bibframe.org/vocab/doi
  • 10.1016/j.dam.2014.03.020
http://localhost/t...ganizacniJednotka
  • 11320
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