| Title: | Domination game |
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| Authors: | ID Brešar, Boštjan (Author)
ID Klavžar, Sandi (Author)
ID Rall, Douglas F. (Author) |
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| Files: |  http://www.imfm.si/preprinti/PDF/01066.pdf
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| Language: | English |
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| Work type: | Not categorized |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | The domination game played on a graph ▫$G$▫ consists of two players, Dominator and Staller who alternate taking turns choosing a vertex from ▫$G$▫ such that whenever a vertex is chosen the graph in as few steps as possible and Staller wishes to delay the process as much as possible. The game domination number ▫$gamma_g(G)$▫ is the number of vertices chosen when Dominator starts the game and the Staller-start game domination number ▫$gamma'_g(G)$▫ when Staller starts the game. It is proved that for any graph ▫$G$▫, ▫$gamma(G) le gamma_g(G) le 2gamma(G) - 1$▫, and that all possible values can be realized. It is also proved that for any graph ▫$G$▫, ▫$gamma_g(G) - 1 le gamma'_g(G) le gamma_g(G) + 2$▫, and that most of the possibilities for mutual values of ▫$gamma_g(G)$▫ and ▫$gamma'_g(G)$▫ can be realized. A connection with Vizing's conjecture is established and several problems and conjectures stated. |
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| Keywords: | teorija grafov, teorija iger, dominantnost, Vizingova domneva, graph theory, game theory, domination, domination game, game domination number, Vizing's conjecture |
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| Year of publishing: | 2009 |
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| Number of pages: | str. 1-14 |
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| Numbering: | Vol. 47, št. 1066 |
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| PID: | 20.500.12556/DKUM-51759  |
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| ISSN: | 1318-4865 |
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| UDC: | 519.17:519.83 |
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| COBISS.SI-ID: | 15032921 |
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| NUK URN: | URN:SI:UM:DK:FIGMXG8Z |
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| Publication date in DKUM: | 10.07.2015 |
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| Views: | 2357 |
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| Downloads: | 43 |
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| Metadata: |    |
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| Categories: | Misc.
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