Pushable chromatic number of graphs with degree constraints

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F21%3A00121466" target="_blank" >RIV/00216224:14330/21:00121466 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1016/j.disc.2020.112151" target="_blank" >https://doi.org/10.1016/j.disc.2020.112151</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.disc.2020.112151" target="_blank" >10.1016/j.disc.2020.112151</a>

Result language

angličtina

Original language name

Pushable chromatic number of graphs with degree constraints

Original language description

Pushable homomorphisms and the pushable chromatic number chi(p) of oriented graphs were introduced by Klostermeyer and MacGillivray in 2004. They notably observed that, for any oriented graph (G) over right arrow, we have chi(p)((G) over right arrow) =.o((G) over right arrow) = 2 chi(p)((G) over right arrow), where chi(p)((G) over right arrow) denotes the oriented chromatic number of -. G. This stands as the first general bounds on chi(p). This parameter was further studied in later works. This work is dedicated to the pushable chromatic number of oriented graphs fulfilling particular degree conditions. For all Lambda &gt;= 29, we first prove that the maximum value of the pushable chromatic number of a connected oriented graph with maximum degree. lies between 2 Delta/2-1 and (Lambda- 3) center dot (Lambda- 1) center dot 2(Delta-1) + 2 which implies an improved bound on the oriented chromatic number of the same family of graphs. For subcubic oriented graphs, that is, when Delta &lt;= 3, we then prove that the maximum value of the pushable chromatic number is 6 or 7. We also prove that the maximum value of the pushable chromatic number of oriented graphs with maximum average degree less than 3 lies between 5 and 6. The former upper bound of 7 also holds as an upper bound on the pushable chromatic number of planar oriented graphs with girth at least 6. (c) 2020 Published by Elsevier B.V.

Czech name

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Czech description

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Type

J_imp - 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

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2021

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Discrete Mathematics

ISSN

0012-365X

e-ISSN

1872-681X

Volume of the periodical

344

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

15

Pages from-to

1-15

UT code for WoS article

000588280100003

EID of the result in the Scopus database

2-s2.0-85092085767