On a Turán-type hypergraph problem of Brown, Erdős and T. Sós

On a Turán-type hypergraph problem of Brown, Erdős and T. Sós

On a Turán-type hypergraph problem of Brown, Erdos and T. Sós

We let G(r)(n,m) denote the set of r-uniform hypergraphs with n vertices and m edges, and f (r)(n, p, s) is the smallestm such that everymember ofG(r)(n,m) contains amember ofG(r)(p, s). In this paper we are interested in the growth of f (r)(n, p, s) for fixed values r, p and s. Brown, Erdős and Sós [Some external problems on r-graphs, in: New Directions in the Theory of Graphs, Proceedings of ...

On An Extremal Hypergraph Problem Of Brown, Erdös And Sós

Let fr(n, v, e) denote the maximum number of edges in an r-uniform hypergraph on n vertices, which does not contain e edges spanned by v vertices. Extending previous results of Ruzsa and Szemerédi and of Erdős, Frankl and Rödl, we partially resolve a problem raised by Brown, Erdős and Sós in 1973, by showing that for any fixed 2 ≤ k < r, we have nk−o(1) < fr(n, 3(r − k) + k + 1, 3) = o(n).

On A Hypergraph Turán Problem Of Frankl

Let C r be the 2k-uniform hypergraph obtained by letting P1, . . . ,Pr be pairwise disjoint sets of size k and taking as edges all sets Pi∪Pj with i =j. This can be thought of as the ‘k-expansion’ of the complete graph Kr: each vertex has been replaced with a set of size k. An example of a hypergraph with vertex set V that does not contain C 3 can be obtained by partitioning V = V1∪V2 and takin...

On an Anti - Ramsey Problem of Burr , Erdős , Graham , and T . Sós Gábor

Given a graph L, in this article we investigate the anti-Ramsey number χS (n,e,L), defined to be the minimum number of colors needed to edge-color some graph G(n,e) with n vertices and e edges so that in every copy of L inG all edges have different colors. We call such a copy of L totally multicolored (TMC). In [7] among many other interesting results and problems, Burr, Erdős, Graham, and T. S...