Parameterized Mixed Graph Coloring

Peter Damaschke ()
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Peter Damaschke: Chalmers University

Journal of Combinatorial Optimization, 2019, vol. 38, issue 2, No 3, 362-374

Abstract: Abstract Coloring of mixed graphs that contain both directed arcs and undirected edges is relevant for scheduling of unit-length jobs with precedence constraints and conflicts. The classic GHRV theorem (attributed to Gallai, Hasse, Roy, and Vitaver) relates graph coloring to longest paths. It can be extended to mixed graphs. In the present paper we further extend the GHRV theorem to weighted mixed graphs. As a byproduct this yields a kernel and a parameterized algorithm (with the number of undirected edges as parameter) that is slightly faster than the brute-force algorithm. The parameter is natural since the directed version is polynomial whereas the undirected version is NP-complete. Furthermore we point out a new polynomial case where the edges form a clique.

Keywords: Graph coloring; Mixed graph; Scheduling; Longest path; Parameterized algorithm (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10878-019-00388-z

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