منابع مشابه
Hamiltonian Maker-Breaker games on small graphs
We look at the unbiased Maker-Breaker Hamiltonicity game played on the edge set of a complete graph Kn, where Maker’s goal is to claim a Hamiltonian cycle. First, we prove that, independent of who starts, Maker can win the game for n = 8 and n = 9. Then we use an inductive argument to show that, independent of who starts, Maker can win the game if and only if n ≥ 8. This, in particular, resolve...
متن کاملGlobal Maker-Breaker games on sparse graphs
In this paper we consider Maker-Breaker games, played on the edges of sparse graphs. For a given graph property P we seek a graph (board of the game) with the smallest number of edges on which Maker can build a subgraph that satisfies P. In this paper we focus on global properties. We prove the following results: 1) for the positive minimum degree game, there is a winning board with n vertices ...
متن کاملMaker-breaker games on random geometric graphs
In a Maker-Breaker game on a graph G, Breaker and Maker alternately claim edges of G. Maker wins if, after all edges have been claimed, the graph induced by his edges has some desired property. We consider four Maker-Breaker games played on random geometric graphs. For each of our four games we show that if we add edges between n points chosen uniformly at random in the unit square by order of ...
متن کاملWalker-Breaker Games
We introduce and analyze the Walker-Breaker game, a variant of Maker-Breaker games where Maker is constrained to choose edges of a walk or path in a given graph G, with the goal of visiting as many vertices of the underlying graph as possible.
متن کاملTripping the HCN Breaker
Hyperpolarization-activated cyclic nucleotide-gated (HCN) channels regulate neuronal excitability, pacemaking, dendritic integration, and homeostatic plasticity and are culprits in aberrant neuronal activity in certain epilepsies. In this issue of Neuron two manuscripts (Santoro et al. and Zolles et al.) report that HCN channel gating and expression are controlled by Trip8b (Pex5R) but with a b...
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ژورنال
عنوان ژورنال: Journal of the Japan Society of Powder and Powder Metallurgy
سال: 1998
ISSN: 0532-8799,1880-9014
DOI: 10.2497/jjspm.45.147