001435956 000__ 05044cam\a2200589\i\4500 001435956 001__ 1435956 001435956 003__ OCoLC 001435956 005__ 20230309004001.0 001435956 006__ m\\\\\o\\d\\\\\\\\ 001435956 007__ cr\cn\nnnunnun 001435956 008__ 210423s2021\\\\sz\a\\\\ob\\\\001\0\eng\d 001435956 019__ $$a1247658567$$a1247667119 001435956 020__ $$a9783030690878$$q(electronic bk.) 001435956 020__ $$a3030690873$$q(electronic bk.) 001435956 020__ $$z9783030690861 001435956 020__ $$z3030690865 001435956 0247_ $$a10.1007/978-3-030-69087-8$$2doi 001435956 035__ $$aSP(OCoLC)1247310115 001435956 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dEBLCP$$dOCLCO$$dOCLCF$$dN$T$$dYDX$$dUKAHL$$dOCLCO$$dOCLCQ$$dCOM$$dOCLCO$$dOCL$$dOCLCQ 001435956 049__ $$aISEA 001435956 050_4 $$aQA95 001435956 08204 $$a793.74$$223 001435956 1001_ $$aBreésar, Boéstjan,$$eauthor. 001435956 24510 $$aDomination games played on graphs /$$cBoéstjan Breésar, Michael A. Henning, Sandi Klavžar, Douglas F. Rall. 001435956 264_1 $$aCham :$$bSpringer,$$c[2021] 001435956 300__ $$a1 online resource (x, 122 pages) :$$billustrations 001435956 336__ $$atext$$btxt$$2rdacontent 001435956 337__ $$acomputer$$bc$$2rdamedia 001435956 338__ $$aonline resource$$bcr$$2rdacarrier 001435956 4901_ $$aSpringerBriefs in mathematics,$$x2191-8198 001435956 504__ $$aIncludes bibliographical references and indexes. 001435956 5050_ $$a1. Introduction -- 2. Domination Game.-3. Total Domination Game -- 4. Games for Staller -- 5. Related Games on Graphs and Hypergraphs.-References.-Symbol Index. 001435956 506__ $$aAccess limited to authorized users. 001435956 520__ $$aThis concise monograph present the complete history of the domination game and its variants up to the most recent developments and will stimulate research on closely related topics, establishing a key reference for future developments. The crux of the discussion surrounds new methods and ideas that were developed within the theory, led by the imagination strategy, the Continuation Principle, and the discharging method of Bujtás, to prove results about domination game invariants. A toolbox of proof techniques is provided for the reader to obtain results on the domination game and its variants. Powerful proof methods such as the imagination strategy are presented. The Continuation Principle is developed, which provides a much-used monotonicity property of the game domination number. In addition, the reader is exposed to the discharging method of Bujtás. The power of this method was shown by improving the known upper bound, in terms of a graph's order, on the (ordinary) domination number of graphs with minimum degree between 5 and 50. The book is intended primarily for students in graph theory as well as established graph theorists and it can be enjoyed by anyone with a modicum of mathematical maturity. The authors include exact results for several families of graphs, present what is known about the domination game played on subgraphs and trees, and provide the reader with the computational complexity aspects of domination games. Versions of the games which involve only the "slow" player yield the Grundy domination numbers, which connect the topic of the book with some concepts from linear algebra such as zero-forcing sets and minimum rank. More than a dozen other related games on graphs and hypergraphs are presented in the book. In all these games there are problems waiting to be solved, so the area is rich for further research. The domination game belongs to the growing family of competitive optimization graph games. The game is played by two competitors who take turns adding a vertex to a set of chosen vertices. They collaboratively produce a special structure in the underlying host graph, namely a dominating set. The two players have complementary goals: one seeks to minimize the size of the chosen set while the other player tries to make it as large as possible. The game is not one that is either won or lost. Instead, if both players employ an optimal strategy that is consistent with their goals, the cardinality of the chosen set is a graphical invariant, called the game domination number of the graph. To demonstrate that this is indeed a graphical invariant, the game tree of a domination game played on a graph is presented for the first time in the literature. . 001435956 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed April 23, 2021). 001435956 650_0 $$aMathematical recreations. 001435956 650_0 $$aGraph theory. 001435956 650_6 $$aJeux mathématiques. 001435956 655_7 $$aPuzzles and games.$$2fast$$0(OCoLC)fst01919958 001435956 655_7 $$aPuzzles and games.$$2lcgft 001435956 655_0 $$aElectronic books. 001435956 7001_ $$aHenning, Michael A.,$$eauthor. 001435956 7001_ $$aKlavžar, Sandi,$$d1962-$$eauthor. 001435956 7001_ $$aRall, Douglas F.,$$eauthor. 001435956 77608 $$iPrint version: $$z3030690865$$z9783030690861$$w(OCoLC)1231956444 001435956 830_0 $$aSpringerBriefs in mathematics.$$x2191-8198 001435956 852__ $$bebk 001435956 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-69087-8$$zOnline Access$$91397441.1 001435956 909CO $$ooai:library.usi.edu:1435956$$pGLOBAL_SET 001435956 980__ $$aBIB 001435956 980__ $$aEBOOK 001435956 982__ $$aEbook 001435956 983__ $$aOnline 001435956 994__ $$a92$$bISE