Reconfiguration graph for vertex colourings of weakly chordal graphs

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Reconfiguration graph for vertex colourings of weakly chordal graphs
Original language description
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 >= 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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