Equitable colorings of bounded treewidth graphs
Theoretical Computer Science - Graph colorings
Exact Algorithms for a Loading Problem with Bounded Clique Width
INFORMS Journal on Computing
Information Sciences: an International Journal
Journal of Discrete Algorithms
Batch processing with interval graph compatibilities between tasks
Discrete Applied Mathematics
Mutual exclusion scheduling with interval graphs or related classes. Part II
Discrete Applied Mathematics
Mutual exclusion scheduling with interval graphs or related classes, Part I
Discrete Applied Mathematics
Scheduling with conflicts: online and offline algorithms
Journal of Scheduling
Solutions to real-world instances of PSPACE-complete stacking
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Scheduling jobs on identical machines with agreement graph
Computers and Operations Research
Efficient algorithms for the double traveling salesman problem with multiple stacks
Computers and Operations Research
Bounded coloring of co-comparability graphs and the pickup and delivery tour combination problem
Theoretical Computer Science
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In this paper, we consider the mutual exclusion scheduling problem for comparability graphs. Given an undirected graph G and a fixed constant m, the problem is to find a minimum coloring of G such that each color is used at most m times. The complexity of this problem for comparability graphs was mentioned as an open problem by Möhring [Problem 9.10, in: I. Rival (Ed.), Graphs and Orders, Reidel, Dordrecht, 1985, p. 583] and for permutation graphs (a subclass of comparability graphs) as an open problem by Lonc [On complexity of some chain and antichain partition problem, in: G. Schmidt, R. Berghammer (Eds.), Graph Theoretical Concepts in Computer Science, WG 91, Lecture Notes in Computer Science, vol. 570, 1999, pp. 97-104]. We prove that this problem is already NP-complete for permutation graphs and for each fixed constant m ≥ 6.