7 papers
Small complete 3-term progression free sets in cyclic groups and vector spaces
Bence Csajbók, Zoltán Lóránt Nagy
A classical extremal problem on progression free sets is to determine the maximum size of a -term arithmetic progression free set in algebraic structures, for instance in interv…
Partitioning the projective plane to two incidence-rich parts
Zoltán Lóránt Nagy
An internal or friendly partition of a vertex set of a graph is a partition to two nonempty sets such that every vertex has at least as many neighbours in its…
Complete -term arithmetic progression free sets of small size in vector spaces and other abelian groups
Bence Csajbók, Zoltán Lóránt Nagy
A subset of an abelian group is called - free if it does not contain a three term arithmetic progression. Moreover, is called complete -…
The double Hall property and cycle covers in bipartite graphs
János Barát, Andrzej Grzesik, Attila Jung +2
In a graph , the -neighborhood of a vertex set consists of all vertices of having at least neighbors in . We say that a bipartite graph satisfies the…
Avoiding intersections of given size in finite affine spaces AG(n,2)
Benedek Kovács, Zoltán Lóránt Nagy
We study the set of intersection sizes of a k-dimensional affine subspace and a point set of size m \in [0, 2^n] of the n-dimensional binary affine space AG(n,2). Following the the…
The extensible No-Three-In-Line problem
Dániel T. Nagy, Zoltán Lóránt Nagy, Russ Woodroofe
The classical No-Three-In-Line problem seeks the maximum number of points that may be selected from an grid while avoiding a collinear triple. The maximum is well known…