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colors for any hexagonal graph 
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doi:10.1016/j.ipl.2004.02.017 
Copyright © 2004 Elsevier B.V. All rights reserved.
2-local 5/4-competitive algorithm for multicoloring triangle-free hexagonal graphs
Received 29 September 2003;
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Abstract
An important optimization problem in the design of cellular networks is to assign sets of frequencies to transmitters to avoid unacceptable interference. A cellular network is generally modeled as a subgraph of the infinite triangular lattice. The distributed frequency assignment problem can be abstracted as a multicoloring problem on a weighted hexagonal graph, where the weight vector represents the number of calls to be assigned at vertices. In this paper we present a 2-local distributed algorithm for multicoloring triangle-free hexagonal graphs using only the local clique numbers ω1(v) and ω2(v) at each vertex v of the given hexagonal graph, which can be computed from local information available at the vertex. We prove that the algorithm uses no more than
colors for any triangle-free hexagonal graph G, without explicitly computing the global clique number ω(G). Hence the competitive ratio of the algorithm is 5/4.
Author Keywords: Graph algorithms; Approximation algorithms; Graph coloring; Frequency planning; Cellular networks; 2-local distributed algorithms
