Star Edge-Coloring of Square Grids
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F21%3A43958634" target="_blank" >RIV/49777513:23520/21:43958634 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.amc.2020.125741" target="_blank" >https://doi.org/10.1016/j.amc.2020.125741</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.amc.2020.125741" target="_blank" >10.1016/j.amc.2020.125741</a>
Alternative languages
Result language
angličtina
Original language name
Star Edge-Coloring of Square Grids
Original language description
A star edge-coloring of a graph G is a proper edge-coloring without bichromatic paths and cycles of length four. The smallest integer k such that G admits a star edge-coloring with k colors is the star chromatic index of G. In the seminal paper on the topic, Dvořák, Mohar, and Šámal asked if the star chromatic index of complete graphs is linear in the number of vertices and gave an almost linear upper bound. Their question remains open, and consequently, to better understand the behavior of the star chromatic index, that parameter has been studied for a number of other classes of graphs. In this paper, we consider star edge-colorings of square grids; namely, the Cartesian products of paths and cycles and the Cartesian products of two cycles. We improve previously established bounds and, as a main contribution, we prove that the star chromatic index of graphs in both classes is either 6 or 7 except for prisms. Additionally, we give a number of exact values for many considered graphs.
Czech name
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Czech description
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Classification
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
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA20-09525S" target="_blank" >GA20-09525S: Structural properties of graph classes characterized by forbidden subgraphs</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
APPLIED MATHEMATICS AND COMPUTATION
ISSN
0096-3003
e-ISSN
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Volume of the periodical
392
Issue of the periodical within the volume
1 March 2021
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
16
Pages from-to
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UT code for WoS article
000594701700017
EID of the result in the Scopus database
2-s2.0-85092911064