Parameterized mixed graph coloring
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| Název: | Parameterized mixed graph coloring |
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| Autoři: | Damaschke, Peter, 1963 |
| Zdroj: | Journal of Combinatorial Optimization. 38(2):362-374 |
| Témata: | longest path, parameterized algorithm, graph coloring, scheduling, mixed graph |
| Popis: | 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. |
| Popis souboru: | electronic |
| Přístupová URL adresa: | https://research.chalmers.se/publication/511193 https://research.chalmers.se/publication/508680 https://research.chalmers.se/publication/511193/file/511193_Fulltext.pdf |
| Databáze: | SwePub |
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Nájsť tento článok vo Web of Science | Abstrakt: | 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. |
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| ISSN: | 15732886 13826905 |
| DOI: | 10.1007/s10878-019-00388-z |