| Title: |
Domatic Number of a Graph and its Variants (Extended Abstract) |
| Authors: |
Adolph, Christoph H.; Akhunzyanov, R.; Alexeev, Maxim G.; Alexeev, G.D.; Amoroso, A.; Andrieux, Vincent; Anosov, V.; Austregesilo, Alexander; Badełek, Barbara; Balestra, Ferruccio; Barth, Jcl.; Baum, Günter; Beck, Reinhard; Bedfer, Yann; Berlin, Asher; Bernhard, Johannes; Bicker, K.; Bielert, Erwin; Bieling, Jakob; Birsa, Renato; Bisplinghoff, Jens; Bodlak, Martin; Böer, Marie; Bordalo, Paula; Bradamante, Franco; Braun, Christopher; Bressan, Andrea; Büchele, M.; Burtin, Etienne; Capozza, Luigi; Chiosso, Michela; Chung, Suhurk; Cicuttin, Andres; Crespo, María Liz; Curiel, Q.; Dalla Torre, Stefano; Dasgupta, Shivaji; Dasgupta, Subinay; Denisov, Oleg Yu; Donskov, Sergey; Doshita, Norihiro; Duic, Venicio; Dünnweber, Wolfgang; Dziewiecki, Michał; Efremov, Anatoli Vasilievich; Elia, C.; Eversheim, Paul Dieter; Eyrich, Wolfgang; Faessler, Martin; Ferrero, Andrea; Finger, Mir; Finger, Mic; Fischer, H.; Franco, Celso; du Fresne von Hohenesche, N.; Friedrich, Jan Michael; Frolov, Vladimir; Gautheron, F.; Gavrichtchouk, O.P.; Gerassimov, S.; Geyer, Reiner; Gnesi, I.; Gobbo, Benigno; Goertz, S.; Gorzellik, M.; Grabmüller, Stefanie; Grasso, Antonino; Grube, Boris; Grussenmeyer, Thomas; Guskov, Alexey; Haas, Florian; von Harrach, Dietrich; Hahne, Devin; Hashimoto, Ryo; Heinsius, F.H.; Herrmann, Felix; Hinterberger, Frank; Höppner, Christian; Horikawa, Naoaki; d'Hose, Nicole; Huber, Stefan; Ishimoto, Shigeru; Ivanov, Andrey; Ivanshin, Yu I.; Iwata, Takashi; Jahn, R.; Jary, Vladimír; Jasinski, Prometeusz Kryspin; Jörg, P.; Joosten, Rainer; Kabuß, Eva Maria; Ketzer, Bernhard; Khaustov, Guennady V.; Khokhlov, Yu A.; Kisselev, Yu F.; Klein, Frank J.; Klimaszewski, Krzysztof S.; Koivuniemi, Jaakko H.; Kolosov, Vladimir N.; Kondo, K.; Königsmann, Kay C.; Konorov, Igor A.; Konstantinov, V.F.; Kotzinian, Aram M.; Kouznetsov, Oleg L.; Krämer, Markus F.; Kroumchtein, Z.V.; Kuchinski, N.; Kunne, Fabienne; Kurek, Krzysztof; Kurjata, Robert P.; Lednev, Anatoly A.; Lehmann, Albert; Levillain, M.; Levorato, Stefano; Lichtenstadt, Jechiel; Maggiora, Angelo; Magnon, Alain; Makke, Nour; Mallot, Gerhard K.; Marchand, Claude; Martin, Anna D.; Marzec, J.; Matoušek, Jindřich; Matsuda, H.; Matsuda, Takeshi; Meshcheryakov, G.; Meyer, Wayne E.; Michigami, T.; Mikhailov, Yu V.; Miyachi, Y.; Nagaytsev, A.; Nagel, Thiemo; Nerling, Frank; Neubert, Sebastian; Neyret, Damien P.; Nový, Josef; Nowak, Wolf Dieter; Nunes, A.S.; Olshevsky, Alexander G.; Orlov, I.; Ostrick, Michael; Panknin, Robert; Panzieri, D.; Parsamyan, Bakur; Paul, Stephan M.; Peshekhonov, Dmitry V.; Platchkov, Stephane K.; Pochodzalla, Jozef.; Polyakov, Vladimir A.; Pretz, J.; Quaresma, Márcia; Quintans, Catarina; Ramos, Saturio; Regali, C.; Reicherz, Gerhard; Rocco, E.; Rossiyskaya, Natalia S.; Ryabchikov, Dmitri I.; Rychter, Andrzej; Samoylenko, Vladimir D.; Sandacz, Andrzej; Sarkar, Subir; Savin, Igor A.; Sbrizzai, Giulio; Schiavon, Paolo G.; Schill, Christian; Schlüter, Tobias; Schmidt, Katharina H.; Schmieden, Hartmut; Schönning, Karin; Schopferer, S.; Schott, Matthias; Shevchenko, O. Yu; Silva, Laura; Sinha, L.; Sirtl, S.; Slunecka, Miloslav; Sosio, S.; Sozzi, Federica; Srnka, Aleš; Steiger, Lukáš; Stolarski, Marcin; Sulej, Robert; Suzuki, Hajime; Szabelski, Adam; Szameitat, T.; Sznajder, Paweł; Takekawa, S.; ter Wolbeek, J.; Tessaro, S.; Tessarotto, F.; Thibaud, F.; Uhl, Sebastian; Uman, Igor U.; Virius, Miroslav; Wang, Li; Weisrock, T.; Wilfert, M.; Windmolders, Roland; Wollny, Heiner; Zaremba, Krzysztof; Zavertyaev, M.; Zemlyanichkina, Elena; Ziembicki, Marcin; Zink, Armin; Šulc, Miroslav; Zelinka, Bohdan |
| Source: |
j-scopus ; j-wok |
| Publisher Information: |
Elsevier Science Bv; Technical university of Liberec, Czech Republic; Technická Univerzita v Liberci |
| Publication Year: |
2015 |
| Description: |
This chapter presents some numerical invariants of graphs that are related to the concept of domination—namely, the domatic number and its variants. The word domatic was coined from the words dominating and chromatic in the same way as the word smog was composed from the words smoke and fog. This concept is a certain analogy of the chromatic number, but instead of independent sets, dominating sets are used in its definition. A subset D of the vertex set V(G) of an undirected graphs G is called dominating if for each x V(G) − D there exists a vertex yD adjacent to x. A domatic partition of G is a partition of V(G), all of whose classes are dominating sets in G. The maximum number of classes of a domatic partition of G is called the “domatic number” of G and denoted by d(G). R. Laskar and S. T. Hedetniemi have introduced the connected domatic number d, (G) of a graph G. It is the maximum number of classes of a partition of V(G) into dominating sets that induce connected subgraphs of G. ; DFG [1102]; German Bundesministerium fur Bildung und Forschung; Czech Republic MEYS [ME492, LA242]; SAIL (CSR), Govt. of India; CERN-RFBR [08-02-91009, 12-02-91500]; Portuguese FCT - Fundacao para a Ciencia e Tecnologia [CERN/FP/109323/2009, CERN/FP/116376/2010, CERN/FP/123600/2011]; MEXT; JSPS [18002006, 20540299, 18540281]; Daiko Foundation; Yamada Foundation; DFG; EU [283286]; Israel Science Foundation; Polish NCN [DEC-2011/01/M/ST2/02350] |
| Document Type: |
article in journal/newspaper |
| File Description: |
text |
| Language: |
English |
| Relation: |
Annals of Discrete Mathematics; https://dspace.tul.cz/handle/15240/16332; https://dspace.tul.cz/handle/15240/13336; https://www.sciencedirect.com/science/article/abs/pii/S0167506008706575 |
| DOI: |
10.1016/j.physletb.2014.11.058 |
| DOI: |
10.1016/S0167-5060(08)70657-5 |
| Availability: |
https://dspace.tul.cz/handle/15240/16332; https://dspace.tul.cz/handle/15240/13336; https://doi.org/10.1016/j.physletb.2014.11.058; https://doi.org/10.1016/S0167-5060(08)70657-5; https://www.sciencedirect.com/science/article/abs/pii/S0167506008706575 |
| Accession Number: |
edsbas.4CFC2FA5 |
| Database: |
BASE |