An O(EV log V) algorithm for finding a maximal weighted matching in general graphs
SIAM Journal on Computing
An introduction to chromatic sums
CSC '89 Proceedings of the 17th conference on ACM Annual Computer Science Conference
On chromatic sums and distributed resource allocation
Information and Computation
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
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 Optimal Cost Chromatic Partition Problem for Trees and Interval Graphs
WG '96 Proceedings of the 22nd International Workshop on Graph-Theoretic Concepts in Computer Science
Coloring of trees with minimum sum of colors
Journal of Graph Theory
The complexity of chromatic strength and chromatic edge strength
Computational Complexity
Minimum sum multicoloring on the edges of trees
Theoretical Computer Science - Approximation and online algorithms
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
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 edge-coloring of regular, bipartite and split graphs
Discrete Applied Mathematics
| Hi-index | 0.04 |
The sum coloring problem asks to find a vertex coloring of a given graph G, using natural numbers, such that the total sum of the colors is minimized. A coloring which achieves this total sum is called an optimum coloring and the minimum number of colors needed in any optimum coloring of a graph is called the strength of the graph. We prove the NP-hardness of finding the vertex strength for graphs with Δ = 6. Polynomial time algorithms are presented for the sum coloring of chain bipartite graphs and k-split graphs. The edge sum coloring problem and the edge strength of a graph are defined similarly. We prove that the edge sum coloring and the edge strength problems are both NP-complete for k-regular graphs, k ≥ 3. Also we give a polynomial time algorithm to solve the edge sum coloring problem on trees.