Partitions of graphs into cographs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F10%3A10081040" target="_blank" >RIV/00216208:11320/10:10081040 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Partitions of graphs into cographs

Popis výsledku v původním jazyce

Cographs form the minimal family of graphs containing K-1 that is closed with respect to complementation and disjoint union. We discuss vertex partitions of graphs into the smallest number of cographs. We introduce a new parameter, calling the minimum order of such a partition the c-chromatic number of the graph. We begin by axiomatizing several well-known graphical parameters as motivation for this function. We present several bounds on c-chromatic number in terms of well-known expressions. We show that if a graph is triangle-free, then its chromatic number is bounded between the c-chromatic number and twice this number. We show that both bounds are sharp for graphs with arbitrarily high girth. This provides an alternative proof to a result by Broereand Mynhardt. We show that any planar graph with girth at least 11 has a c-chromatic number at most two. We close with several remarks on computational complexity; in particular, that computing the c-chromatic number is NP-complete for pl

Název v anglickém jazyce

Partitions of graphs into cographs

Popis výsledku anglicky

Cographs form the minimal family of graphs containing K-1 that is closed with respect to complementation and disjoint union. We discuss vertex partitions of graphs into the smallest number of cographs. We introduce a new parameter, calling the minimum order of such a partition the c-chromatic number of the graph. We begin by axiomatizing several well-known graphical parameters as motivation for this function. We present several bounds on c-chromatic number in terms of well-known expressions. We show that if a graph is triangle-free, then its chromatic number is bounded between the c-chromatic number and twice this number. We show that both bounds are sharp for graphs with arbitrarily high girth. This provides an alternative proof to a result by Broereand Mynhardt. We show that any planar graph with girth at least 11 has a c-chromatic number at most two. We close with several remarks on computational complexity; in particular, that computing the c-chromatic number is NP-complete for pl

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/1M0545" target="_blank" >1M0545: Institut Teoretické Informatiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2010

Kód důvěrnosti údajů

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

Název periodika

Discrete Mathematics

ISSN

0012-365X

e-ISSN

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Svazek periodika

310

Číslo periodika v rámci svazku

24

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

9

Strana od-do

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Kód UT WoS článku

000284251900001

EID výsledku v databázi Scopus

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