Geodesic
3-consecutive c-colorings of graphs
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 3, pp. 393-405

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A 3-consecutive C-coloring of a graph G = (V,E) is a mapping φ:V → ℕ such that every path on three vertices has at most two colors. We prove general estimates on the maximum number (χ̅)_3CC(G) of colors in a 3-consecutive C-coloring of G, and characterize the structure of connected graphs with (χ̅)_3CC(G) ≥ k for k = 3 and k = 4.
Keywords: graph coloring, vertex coloring, consecutive coloring, upper chromatic number 
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Bujtás, Csilla; Sampathkumar, E.; Tuza, Zsolt; Subramanya, M.; Dominic, Charles. 3-consecutive c-colorings of graphs. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 3, pp. 393-405. http://geodesic.mathdoc.fr/item/DMGT_2010_30_3_a3/