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Weak saturation of the cube in the clique ★
Problem
Determine .
Keywords: bootstrap percolation; hypercube; Weak saturation
Convex Equipartitions with Extreme Perimeter ★★
Author(s): Nandakumar
To divide a given 2D convex region C into a specified number n of convex pieces all of equal area (perimeters could be different) such that the total perimeter of pieces is (1) maximized (2) minimized.
Remark: It appears maximizing the total perimeter is the easier problem.
Keywords: convex equipartition
Turán Problem for $10$-Cycles in the Hypercube ★★
Author(s): Erdos
Problem Bound the extremal number of
in the hypercube.
![$ C_{10} $](/files/tex/11903dbe89daae659b28a8bead9b43cae2995c3d.png)
Keywords: cycles; extremal combinatorics; hypercube