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Some remarks on odd edge colorings of digraphs
ID Petruševski, Mirko (Author), ID Škrekovski, Riste (Author)

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Abstract
The principal aim of this article is to initiate a study of the following coloring notion for digraphs. An odd k-edge coloring of a general digraph (directed pseudograph) D is a (not necessarily proper) coloring of its edges with at most k colors such that for every vertex v and color c holds: if c is used on the set ∂$_D$(v) of edges incident with v, then c appears an odd number of times on each non-empty set from the pair ∂$^+_D$(v), ∂$^−_D$(v) of, respectively, outgoing and incoming edges incident with v. We show that it can be decided in polynomial time whether D admits an odd 2-edge coloring. Throughout the paper, several conjectures, questions and open problems are posed. In particular, we conjecture that for each odd edge-colorable digraph four colors suffice.

Language:English
Keywords:digraph, odd edge coloring, odd chromatic index
Work type:Article
Typology:1.01 - Original Scientific Article
Organization:FMF - Faculty of Mathematics and Physics
Publication status:Published
Publication version:Version of Record
Year:2021
Number of pages:10 str.
Numbering:Vol. 9, iss. 3, art. 231
PID:20.500.12556/RUL-134879 This link opens in a new window
UDC:519.17
ISSN on article:2227-7390
DOI:10.3390/math9030231 This link opens in a new window
COBISS.SI-ID:49625347 This link opens in a new window
Publication date in RUL:10.02.2022
Views:747
Downloads:1268
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Record is a part of a journal

Title:Mathematics
Shortened title:Mathematics
Publisher:MDPI AG
ISSN:2227-7390
COBISS.SI-ID:523267865 This link opens in a new window

Licences

License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Licensing start date:01.02.2021

Secondary language

Language:Slovenian
Keywords:digraf, liho povezavno barvanje, lihi kromatični indeks

Projects

Funder:ARRS - Slovenian Research Agency
Project number:P1-0383
Name:Kompleksna omrežja

Funder:ARRS - Slovenian Research Agency
Project number:J1-1692
Name:Barvanja, dekompozicije in pokritja grafov

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