Locally injective k-colourings of planar graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10282425" target="_blank" >RIV/00216208:11320/14:10282425 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.dam.2014.03.020" target="_blank" >http://dx.doi.org/10.1016/j.dam.2014.03.020</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.dam.2014.03.020" target="_blank" >10.1016/j.dam.2014.03.020</a>

Result language
angličtina
Original language name
Locally injective k-colourings of planar graphs
Original language 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).
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
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Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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