10.46298/dmtcs.5798
https://dmtcs.episciences.org/5798
Bensmail, Julien
Julien
Bensmail
Fioravantes, Foivos
Foivos
Fioravantes
On BMRN*-colouring of planar digraphs
In a recent work, Bensmail, Blanc, Cohen, Havet and Rocha, motivated by applications for TDMA scheduling problems, have introduced the notion of BMRN*-colouring of digraphs, which is a type of arc-colouring with particular colouring constraints. In particular, they gave a special focus to planar digraphs. They notably proved that every planar digraph can be 8-BMRN*-coloured, while there exist planar digraphs for which 7 colours are needed in a BMRN*-colouring. They also proved that the problem of deciding whether a planar digraph can be 3-BMRN*-coloured is NP-hard. In this work, we pursue these investigations on planar digraphs, in particular by answering some of the questions left open by the authors in that seminal work. We exhibit planar digraphs needing 8 colours to be BMRN*-coloured, thus showing that the upper bound of Bensmail, Blanc, Cohen, Havet and Rocha cannot be decreased in general. We also generalize their complexity result by showing that the problem of deciding whether a planar digraph can be k-BMRN*-coloured is NP-hard for every k ∈ {3,...,6}. Finally, we investigate the connection between the girth of a planar digraphs and the least number of colours in its BMRN*-colourings.
episciences.org
BMRN*-colouring
planar digraphs
TDMA scheduling
[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
2021-01-25
2021-02-25
2021-02-25
en
journal article
https://hal.archives-ouvertes.fr/hal-02195028v6
1365-8050
https://dmtcs.episciences.org/5798/pdf
VoR
application/pdf
Discrete Mathematics & Theoretical Computer Science
vol. 23 no. 1
Graph Theory
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