Máté Vizer

Coloring Points with Respect to Squares

We consider the problem of 2-coloring geometric hypergraphs. Specifically, we show that there is a constant m such that any finite set of points in the plane

Finding a majority ball with majority answers

{\mathcal {S}} \subset {\mathbb {R}}^2

Finding a non-minority ball with majority answers

S⊂R2 can be 2-colored such that every axis-parallel square that contains at least m points from

On the size of planarly connected crossing graphs

{\mathcal {S}}

Grundy dominating sequences and zero forcing sets

S contains points of both colors. Our proof is constructive, that is, it provides a polynomial-time algorithm for obtaining such a 2-coloring. By affine transformations this result immediately applies also when considering 2-coloring points with respect to homothets of a fixed parallelogram.

The minimum number of vertices in uniform hypergraphs with given domination number

There are many generalizations of the Erd?s-Ko-Rado theorem. Here the new results (and problems) concern families of t -intersecting k -element multisets of an n -set. We point out connections to coding theory and geometry. We verify the conjecture that for n ? t ( k - t ) + 2 such a family can have at most ( n + k - t - 1 k - t ) members.