More complicated questions about maxima and minima, and some closures of NP
Theoretical Computer Science
An introduction to chromatic sums
CSC '89 Proceedings of the 17th conference on ACM Annual Computer Science Conference
SIAM Journal on Computing
Precoloring extension. I: Interval graphs
Discrete Mathematics - Special volume (part 1) to mark the centennial of Julius Petersen's “Die theorie der regula¨ren graphs”
Scheduling with incompatible jobs
Discrete Applied Mathematics
On the cost-chromatic number of graphs
Discrete Mathematics
The membership problem in jump systems
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
On chromatic sums and distributed resource allocation
Information and Computation
Information Processing Letters
Minimum color sum of bipartite graphs
Journal of Algorithms
Routing with Minimum Wire Length in the Dogleg-Free Manhattan Model is $\cal NP$-Complete
SIAM Journal on Computing
Minimal coloring and strength of graphs
Discrete Mathematics
Edge-chromatic sum of trees and bounded cyclicity graphs
Information Processing Letters
MFCS '94 Proceedings of the 19th International Symposium on Mathematical Foundations of Computer Science 1994
A 27/26-Approximation Algorithm for the Chromatic Sum Coloring of Bipartite Graphs
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Two remarks on the power of counting
Proceedings of the 6th GI-Conference on Theoretical Computer Science
Alternating and empty alternating auxiliary stack automata
Theoretical Computer Science
Discrete Applied Mathematics
A short proof of the NP-completeness of minimum sum interval coloring
Operations Research Letters
Complexity results for minimum sum edge coloring
Discrete Applied Mathematics
Note: A note on the strength and minimum color sum of bipartite graphs
Discrete Applied Mathematics
Minimum sum edge colorings of multicycles
Discrete Applied Mathematics
Equality of domination and transversal numbers in hypergraphs
Discrete Applied Mathematics
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The sum of a coloring is the sum of the colors assigned to the vertices (assuming that the colors are positive integers). The sum 驴 (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 驴 (G). For every k, we determine the complexity of the question "Is s(G) 驴 k?": it is coNP-complete for k = 2 and 驴2p-complete for every fixed k 驴 3. We also study the complexity of the edge coloring version of the problem, with analogous definitions for the edge sum 驴驴(G) and the chromatic edge strength s驴(G). We show that for every k 驴 3, it is 驴2p-complete to decide whether s驴(G) 驴 k. As a first step of the proof, we present graphs for every r 驴 3 with chromatic index r and edge strength r + 1. For some values of r, such graphs have not been known before.