Discussiones Mathematicae Graph Theory 26(3) (2006) 369-376
doi: 10.7151/dmgt.1329

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Gábor Bacsó  and  Zsolt Tuza

Computer and Automation Institute
Hungarian Academy of Sciences
H-1111 Budapest, Kende u. 13-17, Hungary


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.

Keywords: graph coloring, cost chromatic number, intersection number of a hypergraph.

2000 Mathematics Subject Classification: Primary: 05C15, 05C62; Secondary: 05C35, 05C65.


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Received 1 December 2005
Revised 19 June 2006