Graphs & digraphs (2nd ed.)
Approximating the Range Sum of a Graph on CREW PRAM
IWDC '02 Proceedings of the 4th International Workshop on Distributed Computing, Mobile and Wireless Computing
The Complexity of Tree Multicolorings
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
The Buffer Minimization Problem for Multiprocessor Scheduling with Conflicts
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
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
Discrete Applied Mathematics
OVSF-CDMA code assignment in wireless ad hoc networks
Proceedings of the 2004 joint workshop on Foundations of mobile computing
The complexity of chromatic strength and chromatic edge strength
Computational Complexity
On Sum Coloring of Graphs with Parallel Genetic Algorithms
ICANNGA '07 Proceedings of the 8th international conference on Adaptive and Natural Computing Algorithms, Part I
Complexity results for minimum sum edge coloring
Discrete Applied Mathematics
A self-stabilizing algorithm for the minimum color sum of a graph
ICDCN'08 Proceedings of the 9th international conference on Distributed computing and networking
Minimum sum edge colorings of multicycles
Discrete Applied Mathematics
Optimal guard sets and the Helly property
European Journal of Combinatorics
Minimum sum set coloring of trees and line graphs of trees
Discrete Applied Mathematics
Max-optimal and sum-optimal labelings of graphs
Information Processing Letters
An effective heuristic algorithm for sum coloring of graphs
Computers and Operations Research
On sum coloring and sum multi-coloring for restricted families of graphs
Theoretical Computer Science
A short proof of the NP-completeness of minimum sum interval coloring
Operations Research Letters
A New Ant Colony Optimization Algorithm for the Lower Bound of Sum Coloring Problem
Journal of Mathematical Modelling and Algorithms
The constraint of difference and total dual integrality
Proceedings of the 17th Panhellenic Conference on Informatics
A memetic algorithm for the Minimum Sum Coloring Problem
Computers and Operations Research
On sum edge-coloring of regular, bipartite and split graphs
Discrete Applied Mathematics
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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 the minimum sum. In fact, we prove that our family gives the smallest trees with this property. Moreover, we show that asymptotically, for each value of k, almost all trees require more than k colors. Finally, we present a linear algorithm for computing the chromatic sum of an arbitrary tree.