The regularity lemma for 3-uniform hypergraphs asserts that every large hypergraph can be decomposed into a bounded number of quasi-random structures consisting of a sub-hypergraph and a sparse underlying graph. In this paper we show that in such a quasi-random structure most pairs of the edges of the graph can be connected by hyperpaths of length at most twelve. Some applications are also given.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics