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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)
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Title
| - Locally injective k-colourings of planar graphs
- Locally injective k-colourings of planar graphs (en)
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skos:prefLabel
| - Locally injective k-colourings of planar graphs
- Locally injective k-colourings of planar graphs (en)
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skos:notation
| - RIV/00216208:11320/14:10282425!RIV15-GA0-11320___
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/00216208:11320/14:10282425
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - Complexity; Planar graph; Graph colouring; Locally injective colouring (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
| - Discrete Applied Mathematics
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
| - Kratochvíl, Jan
- Siggers, Mark
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http://linked.open...ain/vavai/riv/wos
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issn
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number of pages
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http://bibframe.org/vocab/doi
| - 10.1016/j.dam.2014.03.020
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http://localhost/t...ganizacniJednotka
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