József Solymosi

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A graph is called H-free if it contains no induced copy of H . We discuss the following question raised by Erdős and Hajnal. Is it true that for every graph H , there exists an ε(H) > 0 such that any H-free graph with n vertices contains either a complete or an empty subgraph of size at least n? We answer this question in the affirmative for a special class(More)
In this paper we give incidence bounds for arrangements of curves in Fq . As an application, we prove a new result that if (x, f(x)) is a Sidon set then either A+A or f(A)+ f(A) should be large. The main goal of the paper is to illustrate the use of graph spectral techniques in additive combinatorics. This is an extended version of the talks I gave in the(More)
Given a system S of simple continuous curves (``strings'') in the plane, we can define a graph GS as follows. Assign a vertex to each curve, and connect two vertices by an edge if and only if the corresponding two curves intersect. GS is called the intersection graph of S. Not every graph is an intersection graph of a system of curves [EET76] (see Fig. 1(More)