An introduction to chromatic sums
CSC '89 Proceedings of the 17th conference on ACM Annual Computer Science Conference
Investigation on interval edge-colorings of graphs
Journal of Combinatorial Theory Series B
On chromatic sums and distributed resource allocation
Information and Computation
Bipartite graphs and their applications
Bipartite graphs and their applications
Minimum color sum of bipartite graphs
Journal of Algorithms
Minimal coloring and strength of graphs
Discrete Mathematics
Approximation results for the optimum cost chromatic partition problem
Journal of Algorithms
Edge-chromatic sum of trees and bounded cyclicity graphs
Information Processing Letters
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
Approximation Algorithms for the Chromatic Sum
Proceedings of the The First Great Lakes Computer Science Conference on Computing in the 90's
The Optimum Cost Chromatic Partition Problem
CIAC '97 Proceedings of the Third Italian Conference on Algorithms and Complexity
Discrete Applied Mathematics
Complexity results for minimum sum edge coloring
Discrete Applied Mathematics
Minimum sum edge colorings of multicycles
Discrete Applied Mathematics
Finding a Maximum Planar Subset of a Set of Nets in a Channel
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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An edge-coloring of a graph G with natural numbers is called a sum edge-coloring if the colors of edges incident to any vertex of G are distinct and the sum of the colors of the edges of G is minimum. The edge-chromatic sum of a graph G is the sum of the colors of edges in a sum edge-coloring of G. It is known that the problem of finding the edge-chromatic sum of an r-regular (r=3) graph is NP-complete. In this paper we give a polynomial time (1+2r(r+1)^2)-approximation algorithm for the edge-chromatic sum problem on r-regular graphs for r=3. Also, it is known that the problem of finding the edge-chromatic sum of bipartite graphs with maximum degree 3 is NP-complete. We show that the problem remains NP-complete even for some restricted class of bipartite graphs with maximum degree 3. Finally, we give upper bounds for the edge-chromatic sum of some split graphs.