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Morrison, Natasha


Graph Theory » Extremal G.T.

Weak saturation of the cube in the clique ★

Author(s): Morrison; Noel

Problem  

Determine $ \text{wsat}(K_n,Q_3) $.

Keywords: bootstrap percolation; hypercube; Weak saturation

Posted by Jon Noel
updated April 6th, 2016
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Combinatorics

Extremal $4$-Neighbour Bootstrap Percolation in the Hypercube ★★

Author(s): Morrison; Noel

Problem   Determine the smallest percolating set for the $ 4 $-neighbour bootstrap process in the hypercube.

Keywords: bootstrap percolation; extremal combinatorics; hypercube; percolation

Posted by Jon Noel
updated September 20th, 2015
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Combinatorics

Saturation in the Hypercube ★★

Author(s): Morrison; Noel; Scott

Question   What is the saturation number of cycles of length $ 2\ell $ in the $ d $-dimensional hypercube?

Keywords: cycles; hypercube; minimum saturation; saturation

Posted by Jon Noel
updated September 20th, 2015
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Combinatorics » Posets

Saturated $k$-Sperner Systems of Minimum Size ★★

Author(s): Morrison; Noel; Scott

Question   Does there exist a constant $ c>1/2 $ and a function $ n_0(k) $ such that if $ |X|\geq n_0(k) $, then every saturated $ k $-Sperner system $ \mathcal{F}\subseteq \mathcal{P}(X) $ has cardinality at least $ 2^{(1+o(1))ck} $?

Keywords: antichain; extremal combinatorics; minimum saturation; saturation; Sperner system

Posted by Jon Noel
updated April 12th, 2014
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