A problem of Erdos and Sos on 3-graphs
Combinatorics
2014-09-22 v2
Abstract
We show that for every positive epsilon there exist positive delta and n_0 such that every 3-uniform hypergraph on n>=n_0 vertices with the property that every k-vertex subset, where k>=delta*n, induces at least (1/4 + epsilon)*{k \choose 3} edges, contains K4- as a subgraph, where K4- is the 3-uniform hypergraph on 4 vertices with 3 edges. This question was originally raised by Erdos and Sos. The constant 1/4 is the best possible.
Cite
@article{arxiv.1303.7372,
title = {A problem of Erdos and Sos on 3-graphs},
author = {Roman Glebov and Daniel Kral and Jan Volec},
journal= {arXiv preprint arXiv:1303.7372},
year = {2014}
}