# Short paths in 3-uniform quasi-random hypergraphs

Discussiones Mathematicae Graph Theory (2004)

- Volume: 24, Issue: 3, page 469-484
- ISSN: 2083-5892

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topJoanna Polcyn. "Short paths in 3-uniform quasi-random hypergraphs." Discussiones Mathematicae Graph Theory 24.3 (2004): 469-484. <http://eudml.org/doc/270693>.

@article{JoannaPolcyn2004,

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.},

author = {Joanna Polcyn},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {hypergraph; path; quasi-randomness; strong regularity lemma},

language = {eng},

number = {3},

pages = {469-484},

title = {Short paths in 3-uniform quasi-random hypergraphs},

url = {http://eudml.org/doc/270693},

volume = {24},

year = {2004},

}

TY - JOUR

AU - Joanna Polcyn

TI - Short paths in 3-uniform quasi-random hypergraphs

JO - Discussiones Mathematicae Graph Theory

PY - 2004

VL - 24

IS - 3

SP - 469

EP - 484

AB - 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.

LA - eng

KW - hypergraph; path; quasi-randomness; strong regularity lemma

UR - http://eudml.org/doc/270693

ER -

## References

top- [1] B. Bollobás, Random Graphs (Academic Press, London, 1985).
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- [7] J. Polcyn, V. Rödl, A. Ruciński and E. Szemerédi, Short paths in quasi-random triple systems with sparse underlying graphs, in preparation. Zbl1091.05009
- [8] B. Nagle and V. Rödl, Regularity properties for triple systems, Random Structures and Algorithms 23 (2003) 264-332, doi: 10.1002/rsa.10094. Zbl1026.05061
- [9] V. Rödl, A. Ruciński and E. Szemerédi, A Dirac-type theorem for 3-uniform hypergraphs, submitted. Zbl1082.05057
- [10] E. Szemerédi, Regular partitions of graphs, in: Problèmes en Combinatoire et Théorie des Graphes, Proc. Colloque Inter. CNRS, (J.-C. Bermond, J.-C. Fournier, M. Las Vergnas, D. Sotteau, eds), (1978) 399-401. Zbl0413.05055

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