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2006
Springer

The complexity of chromatic strength and chromatic edge strength

9 years 10 months ago
The complexity of chromatic strength and chromatic edge strength
The sum of a coloring is the sum of the colors assigned to the vertices (assuming that the colors are positive integers). The sum (G) of graph G is the smallest sum that can be achieved by a proper vertex coloring of G. The chromatic strength s(G) of G is the minimum number of colors that is required by a coloring with sum (G). For every k, we determine the complexity of the question "Is s(G) k?": it is coNP-complete for k = 2 and p 2-complete for every fixed k 3. We also study the complexity of the edge coloring version of the problem, with analogous definitions for the edge sum (G) and the chromatic edge strength s (G). We show that for every k 3, it is p 2-complete to decide whether s (G) k holds. As a first step of the proof, we present
Dániel Marx
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where CC
Authors Dániel Marx
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