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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

5 votes
1 answer
315 views

Finding a semi-sparse vertex in a grid

Let $H$ be a $r \times r$ grid. Suppose that at most $r/10^5$ vertices of this grid are colored red. For every vertex $v \in V(H)$, let $B_i(v)$ be the ball of radius $i$ centered at $v$. (Or for simp …