Abstract
Let f( G) be the maximum number of colors in a vertex coloring of a simple plane graph G such that no face has distinct colors on all its vertices. If G has n vertices and chromatic number k, then f( G)⩾⌈ n/ k⌉+1. For k∈{2,3}, this bound is sharp for all n (except n⩽3 when k=2). For k=4, the bound is within 1 for all n.
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