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
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
Graphs and Hypergraphs
The maximum saving partition problem
Operations Research Letters
Weighted coloring: further complexity and approximability results
Information Processing Letters
On the Maximum Edge Coloring Problem
Approximation and Online Algorithms
Weighted coloring on planar, bipartite and split graphs: Complexity and approximation
Discrete Applied Mathematics
Weighted Coloring: further complexity and approximability results
Information Processing Letters
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
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
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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-complete 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-complete in P8-free bipartite graphs, but polynomial for P5-free bipartite graphs We next focus ourselves 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-complete, even in the case where the input-graph is both cubic and planar Furthermore, we provide an inapproximability bound of 7/6 – ε, for any ε 0 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.