Abstract.
Let G be a graph with a fixed orientation and let A be a group. Let F(G,A) denote the set of all functions f: E(G) ↦A. The graph G is A -colorable if for any function f∈F(G,A), there is a function c: V(G) ↦A such that for every directed e=u v∈E(G), c(u)−c(v)≠f(e). The group chromatic numberχ1(G) of a graph G is the minimum m such that G is A-colorable for any group A of order at least m under a given orientation D.
In [J. Combin. Theory Ser. B, 56 (1992), 165–182], Jaeger et al. proved that if G is a simple planar graph, then χ1(G)≤6. We prove in this paper that if G is a simple graph without a K 5-minor, then χ1(G)≤5.
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Received: August 18, 1999 Final version received: December 12, 2000
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Lai, HJ., Zhang, X. Group Chromatic Number of Graphs without K5-Minors. Graphs Comb 18, 147–154 (2002). https://doi.org/10.1007/s003730200009
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DOI: https://doi.org/10.1007/s003730200009