In a graph, by definition, the weight of a (proper) coloring with positive integers is the sum of the colors. The chromatic sum is the minimum weight, taken over all the proper colorings. The minimum number of colors in a coloring of minimum weight is the cost chromatic number or strength of the graph. We derive general upper bounds for the strength, in terms of a new parameter of representations by edge intersections of hypergraphs.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1329,
author = {G\'abor Bacs\'o and Zsolt Tuza},
title = {The cost chromatic number and hypergraph parameters},
journal = {Discussiones Mathematicae Graph Theory},
volume = {26},
year = {2006},
pages = {369-376},
zbl = {1135.05019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1329}
}
Gábor Bacsó; Zsolt Tuza. The cost chromatic number and hypergraph parameters. Discussiones Mathematicae Graph Theory, Tome 26 (2006) pp. 369-376. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1329/
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