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Generalized colorings of outerplanar and planar graphs. (English) Zbl 0571.05017
Graph theory with applications to algorithms and computer science, Proc. 5th Int. Conf., Kalamazoo/Mich. 1984, 151-161 (1985).
The F-chromatic number F(G) of a graph G is the minimum number of subsets into which the vertex set of G can be partitioned in such a way that nontrivial graph G is not an induced subgraph of the subgraph induced by each partition class. There are characterized, for \(i=1,2,3\), the graphs F for which F(G)\(\leq i\) for all outerplanar G (all planar G, for \(i=1,2,3,4)\).
Reviewer: J.Fiamčík

MSC:
05C15 Coloring of graphs and hypergraphs
05C10 Planar graphs; geometric and topological aspects of graph theory