On Ramsey minimal graphs.
Constructive upper bounds for cycle-saturated graphs of minimum size.
On families of weakly dependent random variables
Let be a family of random independent k-element subsets of [n] = 1,2,...,n and let denote a family of ℓ-element subsets of [n] such that the event that S belongs to depends only on the edges of contained in S. Then, the edges of are ’weakly dependent’, say, the events that two given subsets S and T are in are independent for vast majority of pairs S and T. In the paper we present some results on the structure of weakly dependent families of subsets obtained in this way. We also list...
On the maximum automorphism group of self-complementary graphs
On random subsets of projective spaces
Small bases for finite groups
On strongly sum-free subsets of abelian groups
In his book on unsolved problems in number theory [1] R. K. Guy asks whether for every natural l there exists with the following property: for every and any n elements of a group such that the product of any two of them is different from the unit element of the group, there exist l of the such that for and . In this note we answer this question in the affirmative in the first non-trivial case when l=3 and the group is abelian, proving the following result.
On the maximal density of sum-free sets
On a problem of Konyagin
Arithmetic progressions of length three in subsets of a random set
On generalized shift graphs
In 1968 Erdős and Hajnal introduced shift graphs as graphs whose vertices are the k-element subsets of [n] = 1,...,n (or of an infinite cardinal κ ) and with two k-sets and joined if . They determined the chromatic number of these graphs. In this paper we extend this definition and study the chromatic number of graphs defined similarly for other types of mutual position with respect to the underlying ordering. As a consequence of our result, we show the existence of a graph with interesting...
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