Locally injective k-colourings of planar graphs

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Locally injective k-colourings of planar graphs

Popis výsledku v původním jazyce

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).

Název v anglickém jazyce

Locally injective k-colourings of planar graphs

Popis výsledku anglicky

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).

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Discrete Applied Mathematics

ISSN

0166-218X

e-ISSN

—

Svazek periodika

173

Číslo periodika v rámci svazku

August

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

9

Strana od-do

53-61

Kód UT WoS článku

000337204100007

EID výsledku v databázi Scopus

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