Domination and fractional domination in digraphs

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Date
2018
Dewey
Principes généraux des mathématiques
Sujet
Graphs and digraphs; Domination; Fractional domination
Journal issue
The Electronic Journal of Combinatorics
Volume
25
Number
3
Publication date
08-2018
Article pages
3.32
DOI
http://dx.doi.org/10.37236/7211
URI
https://basepub.dauphine.fr/handle/123456789/20742
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Author
Harutyunyan, Ararat
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Le, Tien-Nam
56663 Institut Universitaire de France [IUF]
Newman, Alantha
74240 Laboratoire des sciences pour la conception, l'optimisation et la production [G-SCOP]
Thomassé, Stéphan
35418 Laboratoire de l'Informatique du Parallélisme [LIP]
56663 Institut Universitaire de France [IUF]
Type
Article accepté pour publication ou publié
Abstract (EN)
In this paper, we investigate the relation between the (fractional) domination number of a digraph G and the independence number of its underlying graph, denoted by α(G). More precisely, we prove that every digraph G has fractional domination number at most 2α(G), and every directed triangle-free digraph G has domination number at most α(G)⋅α(G)!. The first bound is sharp.