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 of colors in a 3-consecutive C-coloring of G, and characterize the structure of connected graphs with for k = 3 and k = 4.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1502, author = {Csilla Bujt\'as and E. Sampathkumar and Zsolt Tuza and M.S. Subramanya and Charles Dominic}, title = {3-consecutive c-colorings of graphs}, journal = {Discussiones Mathematicae Graph Theory}, volume = {30}, year = {2010}, pages = {393-405}, zbl = {1217.05087}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1502} }
Csilla Bujtás; E. Sampathkumar; Zsolt Tuza; M.S. Subramanya; Charles Dominic. 3-consecutive c-colorings of graphs. Discussiones Mathematicae Graph Theory, Tome 30 (2010) pp. 393-405. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1502/
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