Abstract
The chromatic sum of a graph is the smallest sum of colors among all proper colorings with natural numbers. The strength of a graph is the minimum number of colors necessary to obtain its chromatic sum. A natural generalization of chromatic sum is optimum cost chromatic partition (OCCP) problem, where the costs of colors can be arbitrary positive numbers. Existing results about chromatic sum, strength of a graph, and OCCP problem are presented together with some recent developments. The focus is on polynomial algorithms for some families of graphs and NP‐completeness issues.
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