Scheduling with incompatible jobs
Discrete Applied Mathematics
Generalized coloring for tree-like graphs
Discrete Applied Mathematics
Master-Slave Strategy and Polynomial Approximation
Computational Optimization and Applications
Graphs and Hypergraphs
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
A hypocoloring model for batch scheduling
Discrete Applied Mathematics
Weighted coloring: further complexity and approximability results
Information Processing Letters
On the probabilistic minimum coloring and minimum k-coloring
Discrete Applied Mathematics
On the Maximum Edge Coloring Problem
Approximation and Online Algorithms
Weighted coloring on planar, bipartite and split graphs: Complexity and approximation
Discrete Applied Mathematics
A hypocoloring model for batch scheduling
Discrete Applied Mathematics
On the probabilistic minimum coloring and minimum k-coloring
Discrete Applied Mathematics
Weighted Coloring: further complexity and approximability results
Information Processing Letters
On the max-weight edge coloring problem
Journal of Combinatorial Optimization
Weighted coloring: further complexity and approximability results
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
Weighted coloring on planar, bipartite and split graphs: complexity and improved approximation
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
The hypocoloring problem: complexity and approximability results when the chromatic number is small
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
A one-to-one correspondence between colorings and stable sets
Operations Research Letters
The maximum saving partition problem
Operations Research Letters
| Hi-index | 0.01 |
A version of weighted coloring of a graph is introduced: each node v of a graph G = (V, E) is provided with a positive integer weight w(v) and the weight of a stable set S of G is w(S) = max{w(v) : v 驴 V 驴 S}. A k-coloring S = (S1, . . . , Sk) of G is a partition of V into k stable sets S1, . . . , Sk and the weight of S is w(S1) + . . . + w(Sk). The objective then is to find a coloring S = (S1, . . . , Sk) of G such that w(S1) + . . . + w(Sk) is minimized. Weighted node coloring is NP-hard for general graphs (as generalization of the node coloring problem). We prove here that the associated decision problems are NP-complete for bipartite graphs, for line-graphs of bipartite graphs and for split graphs. We present approximation results for general graphs. For the other families of graphs dealt, properties of optimal solutions are discussed and complexity and approximability results are presented.