Reconfiguration graph for vertex colourings of weakly chordal graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10420121" target="_blank" >RIV/00216208:11320/20:10420121 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=XHHsm.4XcA" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=XHHsm.4XcA</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.disc.2019.111733" target="_blank" >10.1016/j.disc.2019.111733</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Reconfiguration graph for vertex colourings of weakly chordal graphs

Popis výsledku v původním jazyce

The reconfiguration graph R-k(G) of the k-colourings of a graph G contains as its vertex set the k-colourings of G and two colourings are joined by an edge if they differ in colour on just one vertex of G. Bonamy et al. (2014) have shown that if G is a k-colourable chordal graph on n vertices, then Rk+1 (G) has diameter O(n(2)), and asked whether the same statement holds for k-colourable perfect graphs. This was answered negatively by Bonamy and Bousquet (2014). In this note, we address this question for k-colourable weakly chordal graphs, a well-known class of graphs that falls between chordal graphs and perfect graphs. We show that for each k &gt;= 3 there is a k-colourable weakly chordal graph G such that Rk+1(G) is disconnected. On the positive side, we introduce a subclass of k-colourable weakly chordal graphs which we call k-colourable compact graphs and show that for each k-colourable compact graph G on n vertices, Rk+1(G) has diameter O(n(2)). We show that this class contains all k-colourable co-chordal graphs and when k = 3 all 3-colourable (P-5, (P-5) over bar, C-5)-free graphs. We also mention some open problems. (C) 2019 Elsevier B.V. All rights reserved.

Název v anglickém jazyce

Reconfiguration graph for vertex colourings of weakly chordal graphs

Popis výsledku anglicky

The reconfiguration graph R-k(G) of the k-colourings of a graph G contains as its vertex set the k-colourings of G and two colourings are joined by an edge if they differ in colour on just one vertex of G. Bonamy et al. (2014) have shown that if G is a k-colourable chordal graph on n vertices, then Rk+1 (G) has diameter O(n(2)), and asked whether the same statement holds for k-colourable perfect graphs. This was answered negatively by Bonamy and Bousquet (2014). In this note, we address this question for k-colourable weakly chordal graphs, a well-known class of graphs that falls between chordal graphs and perfect graphs. We show that for each k &gt;= 3 there is a k-colourable weakly chordal graph G such that Rk+1(G) is disconnected. On the positive side, we introduce a subclass of k-colourable weakly chordal graphs which we call k-colourable compact graphs and show that for each k-colourable compact graph G on n vertices, Rk+1(G) has diameter O(n(2)). We show that this class contains all k-colourable co-chordal graphs and when k = 3 all 3-colourable (P-5, (P-5) over bar, C-5)-free graphs. We also mention some open problems. (C) 2019 Elsevier B.V. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2020

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

—

Svazek periodika

343

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

6

Strana od-do

111733

Kód UT WoS článku

000510947800012

EID výsledku v databázi Scopus

2-s2.0-85075264930