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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • 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

  • UT code for WoS article

    000594701700017

  • EID of the result in the Scopus database

    2-s2.0-85092911064