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Some remarks on odd edge colorings of digraphs
ID
Petruševski, Mirko
(
Author
),
ID
Škrekovski, Riste
(
Author
)
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https://www.mdpi.com/2227-7390/9/3/231
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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
UDC:
519.17
ISSN on article:
2227-7390
DOI:
10.3390/math9030231
COBISS.SI-ID:
49625347
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
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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