A Brooks-like result for graph powers

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F24%3A00139278" target="_blank" >RIV/00216224:14330/24:00139278 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.ejc.2023.103822" target="_blank" >https://doi.org/10.1016/j.ejc.2023.103822</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2023.103822" target="_blank" >10.1016/j.ejc.2023.103822</a>

Result language
angličtina
Original language name
A Brooks-like result for graph powers
Original language description
Coloring a graph G consists in finding an assignment of colors c : V(G) -> {1, ... , p} such that any pair of adjacent vertices receives different colors. The minimum integer p such that a coloring exists is called the chromatic number of G, denoted by chi(G). We investigate the chromatic number of powers of graphs, i.e. the graphs obtained from a graph G by adding an edge between every pair of vertices at distance at most k. For k = 1, Brooks' theorem states that every connected graph of maximum degree increment 3 except the clique on increment + 1 vertices can be colored using increment colors (i.e. one color less than the naive upper bound). For k 2, a similar result holds: except for Moore graphs, the naive upper bound can be lowered by 2. We prove that for k 3 and for every increment , we can actually spare k-2 colors, except for a finite number of graphs. We then improve this value to Theta(( increment - 1)k12). (c) 2023 Elsevier Ltd. 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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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