Game, set, and graph
نویسندگان
چکیده
منابع مشابه
A Graph-Grabbing Game
Two players share a connected graph with non-negative weights on the vertices. They alternately take the vertices (one in each turn) and collect their weights. The rule they have to obey is that the remaining part of the graph must be connected after each move. We conjecture that the first player can get at least half of the weight of any tree with an even number of vertices. We provide a strat...
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Two players compete in a contest where the first player to win a specified number of points wins the game, and the first player to win a specified number of games wins the set. This paper proves two generalized inequalities, each independent of the probability of winning a point, concerning the better player’s chances of winning. Counterexamples are given for two additional conjectured inequali...
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In the graph distance game, two players alternate in constructing a maximal path. The objective function is the distance between the two endpoints of the path, which one player tries to maximize and the other tries to minimize. In this paper we examine the distance game for various graph operations: the join, the corona and the lexicographic product of graphs. We provide general bounds and exac...
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In the Set Coincidence Game G(V, W), two players alternately choose elements not previously chosen from a finite, nonempty set V, and W is a given family of nonempty subsets of V (the ‘winning sets’). The winner is that player who first adds an element to the set of ‘chosen’ elements 5, so that S E W. This game is closely related to and generalizes Ringeisen’s Isolation Game on graphs. We devel...
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The stationary set splitting game is a game of perfect information of length ω1 between two players, unsplit and split, in which unsplit chooses stationarily many countable ordinals and split tries to continuously divide them into two stationary pieces. We show that it is possible in ZFC to force a winning strategy for either player, or for neither. This gives a new counterexample to Σ2 maximal...
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ژورنال
عنوان ژورنال: BSHM Bulletin: Journal of the British Society for the History of Mathematics
سال: 2018
ISSN: 1749-8430,1749-8341
DOI: 10.1080/17498430.2018.1504458