Short paths in quasi-random triple systems with sparse underlying graphs

Joanna Polcyn, Vojtech Rödl, Andrzej Ruciński, E. Szemerédi

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)584-607
Number of pages24
JournalJournal of Combinatorial Theory. Series B
Volume96
Issue number4
DOIs
Publication statusPublished - Jul 2006

Fingerprint

Random Structure
Random Systems
Triple System
Sparse Graphs
Hypergraph
Shortest path
Regularity Lemma
Uniform Hypergraph
Graph in graph theory

Keywords

  • Paths
  • Quasi-randomness
  • Triple systems

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Short paths in quasi-random triple systems with sparse underlying graphs. / Polcyn, Joanna; Rödl, Vojtech; Ruciński, Andrzej; Szemerédi, E.

In: Journal of Combinatorial Theory. Series B, Vol. 96, No. 4, 07.2006, p. 584-607.

Research output: Contribution to journalArticle

Polcyn, Joanna ; Rödl, Vojtech ; Ruciński, Andrzej ; Szemerédi, E. / Short paths in quasi-random triple systems with sparse underlying graphs. In: Journal of Combinatorial Theory. Series B. 2006 ; Vol. 96, No. 4. pp. 584-607.
@article{b33572495d4f4f988c1da3d41d680e6a,
title = "Short paths in quasi-random triple systems with sparse underlying graphs",
abstract = "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.",
keywords = "Paths, Quasi-randomness, Triple systems",
author = "Joanna Polcyn and Vojtech R{\"o}dl and Andrzej Ruciński and E. Szemer{\'e}di",
year = "2006",
month = "7",
doi = "10.1016/j.jctb.2005.12.002",
language = "English",
volume = "96",
pages = "584--607",
journal = "Journal of Combinatorial Theory. Series B",
issn = "0095-8956",
publisher = "Academic Press Inc.",
number = "4",

}

TY - JOUR

T1 - Short paths in quasi-random triple systems with sparse underlying graphs

AU - Polcyn, Joanna

AU - Rödl, Vojtech

AU - Ruciński, Andrzej

AU - Szemerédi, E.

PY - 2006/7

Y1 - 2006/7

N2 - 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.

AB - 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.

KW - Paths

KW - Quasi-randomness

KW - Triple systems

UR - http://www.scopus.com/inward/record.url?scp=33646768979&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646768979&partnerID=8YFLogxK

U2 - 10.1016/j.jctb.2005.12.002

DO - 10.1016/j.jctb.2005.12.002

M3 - Article

AN - SCOPUS:33646768979

VL - 96

SP - 584

EP - 607

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

IS - 4

ER -