The maximum number of edges in 2K2-free graphs of bounded degree
Discrete Mathematics
Discrete Applied Mathematics - Combinatorial Optimization
Scheduling with incompatible jobs
Discrete Applied Mathematics
A coloring problem for weighted graphs
Information Processing Letters
Combinatorial optimization
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Weighted Node Coloring: When Stable Sets Are Expensive
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Buffer minimization using max-coloring
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Graphs and Hypergraphs
Weighted coloring: further complexity and approximability results
Information Processing Letters
Time slot scheduling of compatible jobs
Journal of Scheduling
Batch processing with interval graph compatibilities between tasks
Discrete Applied Mathematics
NP-completeness of list coloring and precoloring extension on the edges of planar graphs
Journal of Graph Theory
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Approximation algorithms for the max-coloring problem
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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 maximum saving partition problem
Operations Research Letters
Approximating the max-edge-coloring problem
Theoretical Computer Science
Improved approximation algorithms for the max-edge coloring problem
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Improved approximation algorithms for the Max Edge-Coloring problem
Information Processing Letters
Clique clustering yields a PTAS for max-coloring interval graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Theoretical Computer Science
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We study complexity and approximation of min weighted node coloring in planar, bipartite and split graphs. We show that this problem is NP-hard in planar graphs, even if they are triangle-free and their maximum degree is bounded above by 4. Then, we prove that min weighted node coloring is NP-hard in P"8-free bipartite graphs, but polynomial for P"5-free bipartite graphs. We next focus on approximability in general bipartite graphs and improve earlier approximation results by giving approximation ratios matching inapproximability bounds. We next deal with min weighted edge coloring in bipartite graphs. We show that this problem remains strongly NP-hard, even in the case where the input graph is both cubic and planar. Furthermore, we provide an inapproximability bound of 7/6-@e, for any @e0 and we give an approximation algorithm with the same ratio. Finally, we show that min weighted node coloring in split graphs can be solved by a polynomial time approximation scheme.