An Introduction to Chromatic Sums

  title={An Introduction to Chromatic Sums},
  author={Ewa Kubicka and Allen J. Schwenk},
  booktitle={ACM Conference on Computer Science},
We introduce the new concept of the chromatic sum of a graph G, the smallest possible total among all proper colorings of G using natural numbers. We show that computing the chromatic sum for arbitrary graphs is an NP-complete problem. Indeed, a polynomial algorithm for the chromatic sum would be easily modified to compute the chromatic number. Even for trees the chromatic sum is far from trivial. We construct a family of trees to demonstrate that for each k, some trees need k colors to achieve… CONTINUE READING
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