Scheduling groups of tasks with precedence constraints on three dedicated processors
Discrete Applied Mathematics
Hard coloring problems in low degree planar bipartite graphs
Discrete Applied Mathematics
Coloring some classes of mixed graphs
Discrete Applied Mathematics
On two coloring problems in mixed graphs
European Journal of Combinatorics
Information Processing Letters
Scheduling with precedence constraints: mixed graph coloring in series-parallel graphs
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
Selective graph coloring in some special classes of graphs
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
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In this note we consider two coloring problems in mixed graphs, i.e., graphs containing edges and arcs, which arise from scheduling problems where disjunctive and precedence constraints have to be taken into account. We show that they are both NP-complete in cubic planar bipartite mixed graphs, which strengthens some results of Ries and de Werra (2008) [9].