Reconfiguring 10-colourings of planar graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10422903" target="_blank" >RIV/00216208:11320/20:10422903 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=1sGnnkFBzP" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=1sGnnkFBzP</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00373-020-02199-0" target="_blank" >10.1007/s00373-020-02199-0</a>

Result language
angličtina
Original language name
Reconfiguring 10-colourings of planar graphs
Original language description
Let ????>=1 be an integer. The reconfiguration graph ????????(????) of the k-colourings of a graph G has as vertex set the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. A conjecture of Cereceda from 2007 asserts that for every integer ℓ>=????+2 and k-degenerate graph G on n vertices, ????ℓ(????) has diameter ????(????2). The conjecture has been verified only when ℓ>=2????+1. We give a simple proof that if G is a planar graph on n vertices, then ????10(????) has diameter at most ????(????+1)/2. Since planar graphs are 5-degenerate, this affirms Cereceda's conjecture for planar graphs in the case ℓ=2????.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GA19-21082S" target="_blank" >GA19-21082S: Graphs and their algebraic properties</a><br>
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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