Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903525 | Electronic Notes in Discrete Mathematics | 2017 | 6 Pages |
Abstract
A galaxy is a forest of directed stars. The notion of galaxy can be related to Facility Location problems as well as wavelength assignment problems in optical networks. Amini et al. [Combinatorics, Probability & Computing, 19(2):161-182, 2010.] and Gonçalves et al. [Discrete Applied Mathematics, 160(6):744-754, 2012.] gave bounds on the minimum number of galaxies needed to cover the arcs of a digraph D, called directed star arboricity (dst(D)). They conjectured that those bounds could be improved such that dst(D)â¤Î(D), for Î(D)â¥3 and dst(D)â¤2Î+(D) for Î+(D)â¥2. In this work, we study the directed star arboricity in two non-trivial digraph classes: k-degenerate digraphs and tournaments.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Henri Perret du Cray, Mourad Baïou, Laurent Beaudou, Vincent Limouzy,