Zoltán Lóránt Nagy

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Let H be a graph on n vertices and let the blow-up graph G[H] be defined as follows. We replace each vertex vi of H by a cluster Ai and connect some pairs of vertices of Ai and Aj if (vi, vj) was an edge of the graph H. As usual, we define the edge density between Ai and Aj as d(Ai, Aj) = e(Ai, Aj) |Ai||Aj | . We study the following problem. Given densities(More)
In this paper we propose a multipartite version of the classical Turán problem of determining the minimum number of edges needed for an arbitrary graph to contain a given subgraph. As it turns out, here the non-trivial problem is the determination of the minimal edge density between two classes that implies the existence of a given subgraph. We determine(More)
We study the function M(n, k) which denotes the number of maximal k-uniform intersecting families F ⊆ ([n] k ) . Improving a bound of Balogh, Das, Delcourt, Liu and Sharifzadeh on M(n, k), we determine the order of magnitude of logM(n, k) by proving that for any fixed k, M(n, k) = nΘ(( 2k k )) holds. Our proof is based on Tuza’s set pair approach. The main(More)
Let F be a family of pairs of sets. We call it an (a, b)-set system if for every set-pair (A,B) in F we have that |A| = a, |B| = b, A ∩ B = ∅. The following classical result on families of cross-intersecting set-pairs is due to Bollobás [6]. Let F be an (a, b)-set system with the cross-intersecting property, i.e., for (Ai, Bi), (Aj, Bj) ∈ F with i 6= j we(More)
In this paper, we study (1 : b) Avoider-Enforcer games played on the edge set of the complete graph on n vertices. For every constant k ≥ 3 we analyse the k-star game, where Avoider tries to avoid claiming k edges incident to the same vertex. We analyse both versions of Avoider-Enforcer games – the strict and the monotone – and for each provide explicit(More)
Starting with a result in combinatorial number theory we prove that (apart from a couple of exceptions that can be classified), for any elements a1, . . . , an of GF (q), there are distinct field elements b1, . . . , bn such that a1b1 + · · ·+ anbn = 0. This implies the classification of hyperplanes lying in the union of the hyperplanes Xi = Xj in a vector(More)