# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2017-2018): c. 84%

# Discussiones Mathematicae Graph Theory

## SHORT PATHS IN 3-UNIFORM QUASI-RANDOM HYPERGRAPHS

Joanna Polcyn

Department of Discrete Mathematics
Poznań

## Abstract

Frankl and Rödl [3] proved a strong regularity lemma for 3-uniform hypergraphs, based on the concept of δ-regularity with respect to an underlying 3-partite graph. In applications of that lemma it is often important to be able to glue" together separate pieces of the desired subhypergraph. With this goal in mind, in this paper it is proved that every pair of typical edges of the underlying graph can be connected by a hyperpath of length at most seven. The typicality of edges is defined in terms of graph and hypergraph neighborhoods, and it is shown that all but a small fraction of edges are indeed typical.

Keywords: hypergraph, path, quasi-randomness.

2000 Mathematics Subject Classification: 05C65, 05C12, 05C38.

## References

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