Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 72
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Georgakopoulos, Agelos Haslegrave, John and Montgomery, Richard 2019. Forcing large tight components in 3-graphs. European Journal of Combinatorics, Vol. 77, Issue. , p. 57.
    Nenadov, Rajko and Škorić, Nemanja 2019. Powers of Hamilton cycles in random graphs and tight Hamilton cycles in random hypergraphs. Random Structures & Algorithms, Vol. 54, Issue. 1, p. 187.
    CZYGRINOW, ANDRZEJ DEBIASIO, LOUIS MOLLA, THEODORE and TREGLOWN, ANDREW 2018. TILING DIRECTED GRAPHS WITH TOURNAMENTS. Forum of Mathematics, Sigma, Vol. 6, Issue. ,
    Allen, Peter Koch, Christoph Parczyk, Olaf and Person, Yury 2018. LATIN 2018: Theoretical Informatics. Vol. 10807, Issue. , p. 28.
    Ferber, Asaf and Nenadov, Rajko 2018. Spanning universality in random graphs. Random Structures & Algorithms, Vol. 53, Issue. 4, p. 604.
    Bustamante, Sebastián Hàn, Hiêp and Stein, Maya 2018. Almost partitioning 2-colored complete 3-uniform hypergraphs into two monochromatic tight or loose cycles. Journal of Graph Theory,
    Garbe, Frederik and Mycroft, Richard 2018. Hamilton cycles in hypergraphs below the Dirac threshold. Journal of Combinatorial Theory, Series B, Vol. 133, Issue. , p. 153.
    de Oliveira Bastos, Josefran Mota, Guilherme Oliveira Schacht, Mathias Schnitzer, Jakob and Schulenburg, Fabian 2017. Loose Hamiltonian Cycles Forced by Large $(k-2)$-Degree---Approximate Version. SIAM Journal on Discrete Mathematics, Vol. 31, Issue. 4, p. 2328.
    Han, Jie Zang, Chuanyun and Zhao, Yi 2017. Minimum vertex degree thresholds for tiling complete 3-partite 3-graphs. Journal of Combinatorial Theory, Series A, Vol. 149, Issue. , p. 115.
    de O. Bastos, J. Mota, G.O. Schacht, M. Schnitzer, J. and Schulenburg, F. 2017. Loose Hamiltonian cycles forced by large (k− 2)-degree - sharp version. Electronic Notes in Discrete Mathematics, Vol. 61, Issue. , p. 101.
    Rödl, Vojtěch Ruciński, Andrzej Schacht, Mathias and Szemerédi, Endre 2017. On the Hamiltonicity of Triple Systems with High Minimum Degree. Annals of Combinatorics, Vol. 21, Issue. 1, p. 95.
    Maherani, L. and Omidi, G.R. 2017. Monochromatic Hamiltonian Berge-cycles in colored hypergraphs. Discrete Mathematics, Vol. 340, Issue. 8, p. 2043.
    Han, Jie 2017. Theory and Applications of Models of Computation. Vol. 10185, Issue. , p. 289.
    Cooley, Oliver and Mycroft, Richard 2017. The minimum vertex degree for an almost-spanning tight cycle in a 3-uniform hypergraph. Discrete Mathematics, Vol. 340, Issue. 6, p. 1172.
    GAO, WEI and HAN, JIE 2017. Minimum Codegree Threshold for C 6 3-Factors in 3-Uniform Hypergraphs. Combinatorics, Probability and Computing, Vol. 26, Issue. 04, p. 536.
    Staden, Katherine and Treglown, Andrew 2017. On Degree Sequences Forcing The Square of a Hamilton Cycle. SIAM Journal on Discrete Mathematics, Vol. 31, Issue. 1, p. 383.
    DeBiasio, Louis and Nelsen, Luke L. 2017. Monochromatic cycle partitions of graphs with large minimum degree. Journal of Combinatorial Theory, Series B, Vol. 122, Issue. , p. 634.
    HAN, JIE LO, ALLAN TREGLOWN, ANDREW and ZHAO, YI 2017. Exact Minimum Codegree Threshold for K − 4-Factors. Combinatorics, Probability and Computing, Vol. 26, Issue. 06, p. 856.
    Lo, Allan Patel, Viresh Skokan, Jozef and Talbot, John 2017. Decomposing tournaments into paths. Electronic Notes in Discrete Mathematics, Vol. 61, Issue. , p. 813.
    Balogh, József Molla, Theodore and Sharifzadeh, Maryam 2016. Triangle factors of graphs without large independent sets and of weighted graphs. Random Structures & Algorithms, Vol. 49, Issue. 4, p. 669.
    Download full list
    ×
  • Get access
    Add to cart USD35.00
    Check if you have access via personal or institutional login
    Log in Register

A Dirac-Type Theorem for 3-Uniform Hypergraphs

  • VOJTĚCH RÖDL (a1), ANDRZEJ RUCIŃSKI (a2) and ENDRE SZEMERÉDI (a3)
Abstract

A Hamiltonian cycle in a 3-uniform hypergraph is a cyclic ordering of the vertices in which every three consecutive vertices form an edge. In this paper we prove an approximate and asymptotic version of an analogue of Dirac's celebrated theorem for graphs: for each γ>0 there exists n0 such that every 3-uniform hypergraph on $n\geq n_0$ vertices, in which each pair of vertices belongs to at least $(1/2+\gamma)n$ edges, contains a Hamiltonian cycle.

Copyright
2006 Cambridge University Press
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed

Cancel
Confirm
×