Abstract
Let G = (V, A, E) denote a finite mixed graph with vertex set V = {v 1, v 1, …, v n }, arc set A, and edge set E. Arc (v i , v j ) ∈ A means ordered pair of vertices, and edge [v p , v q ] ∈ E means unordered pair of vertices. Mixed graph coloring ψ may be defined as follows (see [3]).
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References
Brucker, P., Kravchenko, S.A., Sotskov, Y.N., (1999), “Preemptive job-shop scheduling problems with a fixed number of jobs”, Math. Meth. Oper. Res., 49, No. 1, 41–76.
Even, S., Itai, A., Shamir, A., (1976), “On the complexity of timetable and multicommodity flow problems”, SIAM J. Comput., 5, No. 4, 691–703.
Hansen, P., Kuplinsky, J., de Werra, D., (1997), “Mixed graph colorings”, Math. Meth. Oper. Res., 45, 145–160.
Hefetz, N., Adiri, I., (1982), “An efficient optimal algorithm for the two-machine, unit-time, job-shop, schedule-length, problem”, Math. Oper. Res., 7, No. 3, 354–360.
Karp, R.M., (1972), “Reducibility among combinatorial problems”, in: R.E. Miller, J.W. Thather, et al., Complexity of Computer Computations, Plenum Press, New York, 85–103.
Lenstra, J.K., Rinnooy Kan, A.H.G., (1979), “Computational complexity of discrete optimization problems”, Ann. Discrete Math., 4, 121–140.
Sotskov, Yu.N., (1991), “The complexity of shop-scheduling problems with two or three jobs”, European J. Oper. Res., 53, 326–336.
Sotskov, Yu.N., Tanaev, V.S., Werner, F. (1998), “Scheduling problems and mixed graph colorings”, Otto-von-Guericke-Universität, Magdeburg, Preprint No. 38.
Tanaev, V.S., Sotskov, Yu.N., Strusevich, V.A., (1994), “Scheduling theory. Multi-stage systems”, Kluwer Academic Publishers, Dordrecht.
Timkowsky, V.G., (1985), “Polynomial-time algorithm for the Lenstra-Rinnooy Kan two-machine scheduling problem”, Kibernetika (Kiev), 2, 109–111 (in Russian).
Williamson, D.P., Hall, L.A., Hoogeveen, J.A., Hurkens, C.A.J., Lenstra, J.K., Sevast’janov, S.V., Shmoys, D.B., (1997), “Short shop schedules”, Oper. Res., 45, No. 2, 288–294.
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Sotskov, Y.N. (2000). Scheduling via Mixed Graph Coloring. In: Inderfurth, K., Schwödiauer, G., Domschke, W., Juhnke, F., Kleinschmidt, P., Wäscher, G. (eds) Operations Research Proceedings 1999. Operations Research Proceedings 1999, vol 1999. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58300-1_64
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DOI: https://doi.org/10.1007/978-3-642-58300-1_64
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