Parameterized mixed graph coloring
Artikel i vetenskaplig tidskrift, 2019
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.
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.
longest path
parameterized algorithm
graph coloring
scheduling
mixed graph
Författare
Peter Damaschke
Chalmers, Data- och informationsteknik, Data Science
Journal of Combinatorial Optimization
1382-6905 (ISSN) 1573-2886 (eISSN)
Vol. 38 2 362-374Fundament
Grundläggande vetenskaper
Ämneskategorier
Datavetenskap (datalogi)
Diskret matematik
DOI
10.1007/s10878-019-00388-z