Coloring of Trees with Minimum Sum of Colors

Details Coloring of Trees with Minimum Sum of Colors Coloring of Trees with Minimum Sum of Colors

1999-04-26

arxiv.org/abs/math/9904140v1

Mathematics

Combinatorics

5 pages, 1 figure

Scientific paper

The chromatic sum of a graph is the smallest sum of colors among all proper
colorings with natural numbers. The strength is the minimum number of colors
needed to achieve the chromatic sum. We construct for each positive integer k a
tree with strength k that has maximum degree only 2k-2. The result is best
possible.

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