Continuous participation of objects in the schedule with the prescribed operations
Daghestan Electronic Mathematical Reports, Tome 2 (2014), pp. 68-74.

Voir la notice de l'article provenant de la source Math-Net.Ru

Effectively verifiable necessary and sufficient conditions for existence of continuous schedule by length 3 were obtained. Some relationships between scheduling, edge coloring and graph matchings were considered.
Keywords: schedule, interval edge coloring, bipartite graph, matching.
@article{DEMR_2014_2_a4,
     author = {A. M. Magomedov},
     title = {Continuous participation of objects in the schedule with the prescribed operations},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {68--74},
     publisher = {mathdoc},
     volume = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2014_2_a4/}
}
TY  - JOUR
AU  - A. M. Magomedov
TI  - Continuous participation of objects in the schedule with the prescribed operations
JO  - Daghestan Electronic Mathematical Reports
PY  - 2014
SP  - 68
EP  - 74
VL  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DEMR_2014_2_a4/
LA  - ru
ID  - DEMR_2014_2_a4
ER  - 
%0 Journal Article
%A A. M. Magomedov
%T Continuous participation of objects in the schedule with the prescribed operations
%J Daghestan Electronic Mathematical Reports
%D 2014
%P 68-74
%V 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DEMR_2014_2_a4/
%G ru
%F DEMR_2014_2_a4
A. M. Magomedov. Continuous participation of objects in the schedule with the prescribed operations. Daghestan Electronic Mathematical Reports, Tome 2 (2014), pp. 68-74. http://geodesic.mathdoc.fr/item/DEMR_2014_2_a4/

[1] Asratian A.S, Casselgren C.J., Some results on interval edge colorings of $(\alpha,\beta)$-biregular bipartite graphs, Department Math., Linkoping University S–581 83, Linkoping, Sweden, 2007 | MR

[2] Even S., Itai A., Shamir A., “On the complexity of timetable and integral multi-commodity flow problems”, SIAM J. Comput., 5:4 (1976), 691–703 | DOI | MR | Zbl

[3] Giaro K., Compact task scheduling on dedicated processors with no waiting period, PhD, Technical University of Gdansk, IETI Faculty, Gdansk, 1999 (in Polish)

[4] Giaro K., “The complexity of consecutive $\Delta$-coloring of bipartite graphs: 4 is easy, 5 is hard”, Ars Combin., 47 (1997), 287–298 | MR | Zbl

[5] Giaro K., Kubale M., Malafiejcki M., “On the deficiency of bipartite graphs”, Discrete Appl. Math., 1999, no. 94, 193–203, Gdansk | DOI | MR | Zbl

[6] Hansen H.M., Scheduling with minimum waiting periods, Master Thesis, Odense University, Odense, Denmark, 1992 (In Danish)

[7] Hanson D., Loten C.O.M., Toft B., “On interval colourings of bi-regular bipartite graphs”, Ars Combinat., 50 (1998), 23–32 | MR | Zbl

[8] Holyer I., “The $NP$-completeness of edge-coloring”, SIAM J. Comput., 10:4 (1981), 718–720 | DOI | MR | Zbl

[9] Asratyan A.S., Kamalyan R.R., “Intervalnye raskraski rëber multigrafa”, Prikladnaya matematika, 5, Izd-vo Erevan. un-ta, Erevan, 1987, 25–34

[10] Vizing V.G, “Ob otsenke khromaticheskogo klassa p-grafa”, Sb. nauch. tr., Diskretnyi analiz, 3, In-t matematiki SO AN SSSR, Novosibirsk, 1964, 25–30

[11] Geri M., Dzhonson D., Vychislitelnye mashiny i trudnoreshaemye zadachi, Per. s angl., Mir, M., 1982 | MR

[12] Lovas L., Plammer M., Prikladnye zadachi teorii grafov. Teoriya parosochetanii v matematike, fizike, khimii, Per. s angl., Mir, M., 1998

[13] Magomedov A.M., K voprosu ob usloviyakh uplotneniya matritsy iz 6 stolbtsov, Dep. v VINITI, M., 1991

[14] Magomedov A.M., Usloviya i algoritm uplotneniya matritsy iz 4 stolbtsov, Dep. v VINITI, No 175-B92, M., 1992

[15] Magomedov A.M., Magomedov T.A., “Intervalnaya na odnoi dole pravilnaya rëbernaya 5-raskraska dvudolnogo grafa”, PDM / Razdel «Prikladnaya teoriya grafov», 2011, no. 5, 85–91 | MR

[16] Magomedov A.M., Sapozhenko A.A., “Usloviya suschestvovaniya nepreryvnykh raspisanii dlitelnosti pyat”, Vestnik MGU, ser. Vychislitelnaya matematika i kibernetika, 2010, no. 1, 39–44 | Zbl

[17] Magomedov A.M., Magomedov T.A., “O prilozhenii algoritma vychisleniya podgrafa maksimalnoi plotnosti k zadache optimizatsii raspisaniya”, Mat. zametki, 93:2 (2013), 313–315 | DOI | Zbl

[18] Ore O., Teoriya grafov, Nauka. Gl. red. fiz.-mat. lit., M., 1980 | MR

[19] Sevastyanov S.V., “Ob intervalnoi raskrashivaemosti rëber dvudolnogo grafa”, Metody diskretnogo analiza, 50 (1990), 61–72 | Zbl

[20] Tanaev V.S., Sotskov Yu.N., Strusevich V.A., Teoriya raspisanii. Mnogostadiinye sistemy, Nauka, M., 1989 | MR