Authors: Julien Bensmail ¹; Thibaut Blanc ²; Nathann Cohen ³; Frédéric Havet ¹; Leonardo Rocha ^4,5

• 1 Combinatorics, Optimization and Algorithms for Telecommunications
• 2 École normale supérieure - Rennes [ENS Rennes]
• 3 Graphes, Algorithmes et Combinatoire (LRI)
• 4 Universidade Estadual do Ceará
• 5 Universidade Estadual do Ceará [Brasil] = State University of Ceará [Brazil] [UECE]

We investigate graph colouring models for the purpose of optimizing TDMA link scheduling in Wireless Networks. Inspired by the BPRN-colouring model recently introduced by Rocha and Sasaki, we introduce a new colouring model, namely the BMRN-colouring model, which can be used to model link scheduling problems where particular types of collisions must be avoided during the node transmissions. In this paper, we initiate the study of the BMRN-colouring model by providing several bounds on the minimum number of colours needed to BMRN-colour digraphs, as well as several complexity results establishing the hardness of finding optimal colourings. We also give a special focus on these considerations for planar digraph topologies, for which we provide refined results.