Majority Choosability of Digraphs

Marcin Anholcer , Bartłomiej Bosek , Jarosław Grytczuk

Abstract

A majority coloring of a digraph is a coloring of its vertices such that for each vertex v, at most half of the out-neighbors of v have the same color as v. A digraph D is majority k-choosable if for any assignment of lists of colors of size k to the vertices there is a majority coloring of D from these lists. We prove that every digraph is majority 4-choosable. This gives a positive answer to a question posed recently by Kreutzer, Oum, Seymour, van der Zypen, and Wood (2017). We obtain this result as a consequence of a more general theorem, in which majority condition is protably extended. For instance, the theorem implies also that every digraph has a coloring from arbitrary lists of size three, in which at most 2=3 of the out-neighbors of any vertex share its color. This solves another problem posed by the same authors, and supports an intriguing conjecture stating that every digraph is majority 3-colorable.
Author Marcin Anholcer (WIiGE / KBO)
Marcin Anholcer,,
- Department of Operations Research
, Bartłomiej Bosek - Uniwersytet Jagielloński w Krakowie (UJ)
Bartłomiej Bosek,,
-
, Jarosław Grytczuk - Warsaw University of Technology (PW), MNiSW [80]
Jarosław Grytczuk,,
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Journal seriesElectronic Journal of Combinatorics, ISSN 1077-8926, (A 25 pkt)
Issue year2017
Vol24
No3
Pages1-5
Publication size in sheets0.5
Keywords in EnglishGraph theory; Graph coloring; List coloring
ASJC Classification1703 Computational Theory and Mathematics; 2608 Geometry and Topology; 2614 Theoretical Computer Science
DOIDOI:10.37236/6923
URL https://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i3p57
Languageen angielski
Score (nominal)25
Score sourcejournalList
ScoreMinisterial score = 25.0, 02-04-2020, ArticleFromJournal
Publication indicators WoS Citations = 1; Scopus SNIP (Source Normalised Impact per Paper): 2017 = 1.062; WoS Impact Factor: 2017 = 0.762 (2) - 2017=0.759 (5)
Citation count*7 (2020-09-23)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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