Majority Choosability of Digraphs
Marcin Anholcer , Bartłomiej Bosek , Jarosław Grytczuk
AbstractA 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.
|Journal series||Electronic Journal of Combinatorics, ISSN 1077-8926, (A 25 pkt)|
|Publication size in sheets||0.5|
|Keywords in English||Graph theory; Graph coloring; List coloring|
|ASJC Classification||; ;|
|Score||= 25.0, 02-04-2020, ArticleFromJournal|
|Publication indicators||= 1; : 2017 = 1.062; : 2017 = 0.762 (2) - 2017=0.759 (5)|
|Citation count*||7 (2020-09-23)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.