An introduction to chromatic sums
CSC '89 Proceedings of the 17th conference on ACM Annual Computer Science Conference
Generalized coloring for tree-like graphs
Discrete Applied Mathematics
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
Journal of Algorithms
Approximation Algorithms for the Chromatic Sum
Proceedings of the The First Great Lakes Computer Science Conference on Computing in the 90's
Multicoloring Planar Graphs and Partial k-Trees
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
The Optimum Cost Chromatic Partition Problem
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Information and Computation
List edge multicoloring in graphs with few cycles
Information Processing Letters
Minimum sum multicoloring on the edges of trees
Theoretical Computer Science - Approximation and online algorithms
Minimum sum set coloring of trees and line graphs of trees
Discrete Applied Mathematics
Polynomial time preemptive sum-multicoloring on paths
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On sum coloring and sum multi-coloring for restricted families of graphs
Theoretical Computer Science
Minimum sum multicoloring on the edges of planar graphs and partial k-trees
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
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The multicoloring problem is that given a graph G and integer demands x(v) for every vertex v, assign a set of x(v) colors to vertex v, such that neighboring vertices have disjoint sets of colors. In the preemptive sum multicoloring problem the finish time of a vertex is defined to be the highest color assigned to it. The goal is to minimize the sum of the finish times. The study of this problem is motivated by applications in scheduling. Answering a question of Halld贸rsson et al. [4], we show that the problem is strongly NP-hard in binary trees. As a first step toward this result we prove that list multicoloring of binary trees is NP-complete.