Oct 10, 2008 · We disprove this conjecture by establishing an n-uniform hypergraph with maximum neighborhood size 3*2^(n-3) where Maker has a winning strategy.

Apr 16, 2009 · We disprove this conjecture by establishing an n-uniform hypergraph with maximum neighborhood size 3*2^(n - 3) where Maker has a winning ...

We disprove this conjecture by establishing an n-uniform hypergraph with maximum neighborhood size 3*2^(n-3) where Maker has a winning strategy. Moreover, we ...

Oct 4, 2012 · We disprove this conjecture by establishing, for every n≥3, the existence of an n-uniform hypergraph with maximum neighborhood size 3·2n−3 where ...

We first prove that the Neighborhood Conjecture, in this strongest of its forms, is not true, even if we require Maker to use a pairing strategy. Theorem 1.7.

We study a Maker/Breaker game described by Beck. As a result we disprove a conjecture of Beck on positional games, establish a connection between this game ...

We disprove this conjecture by establishing an n-uniform hypergraph with maximum neighborhood size 3 ·2 n − 3 where Maker has a winning strategy. Moreover, we ...

Bibliographic details on Disproving the Neighborhood Conjecture.

Our results have implications on Maker/Breaker games and SAT: We disprove a conjecture of Beck on positional games and construct an unsatisfiable k -CNF formula ...

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