The channel assignment problem for mutually adjacent sites
Journal of Combinatorial Theory Series A
Graph labeling and radio channel assignment
Journal of Graph Theory
2-Local 5/4-competitive algorithm for multicoloring triangle-free hexagonal graphs
Information Processing Letters
2-local 4/3-competitive algorithm for multicoloring hexagonal graphs
Journal of Algorithms
1-local 33/24-competitive algorithm for multicoloring hexagonal graphs
WAW'11 Proceedings of the 8th international conference on Algorithms and models for the web graph
A linear time algorithm for 7-[3]coloring triangle-free hexagonal graphs
Information Processing Letters
Every triangle-free induced subgraph of the triangular lattice is (5m,2 m)-choosable
Discrete Applied Mathematics
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A basic problem in the design of mobile telephone networks is to assign sets of radio frequency bands (colours) to transmitters (vertices) to avoid interference. Often the transmitters are laid out like vertices of a triangular lattice in the plane. We investigate the corresponding colouring problem of assigning sets of colours of size p(υ) to each vertex of the triangular lattice so that the sets of colours assigned to adjacent vertices are disjoint. A n-[p]colouring of a graph G is a mapping c from V(G) into the set of the subsets of {1,2,...,n} such that |c(υ)|=p(υ) and for any adjacent vertices u and υ, c(u)∩c(υ)=φ. We give here an alternative proof of the fact that every triangular-free induced subgraph of the triangular lattice is 5-[2]colourable. This proof yields a constant time distributed algorithm that finds a 5-[2]colouring of such a graph. We then give a distributed algorithm that finds a [p]colouring of a triangle-free induced subgraph of the triangular lattice with at most 5ωp(G)/4 + 3 colours.