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2004 | 24 | 3 | 469-484
Tytuł artykułu

Short paths in 3-uniform quasi-random hypergraphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Wydawca
Rocznik
Tom
24
Numer
3
Strony
469-484
Opis fizyczny
Daty
wydano
2004
otrzymano
2003-06-18
poprawiono
2004-01-21
Twórcy
  • Department of Discrete Mathematics, Adam Mickiewicz University, Poznań
Bibliografia
  • [1] B. Bollobás, Random Graphs (Academic Press, London, 1985).
  • [2] Y. Dementieva, Equivalent Conditions for Hypergraph Regularity (Ph.D. Thesis, Emory University, 2001).
  • [3] P. Frankl and V. Rödl, Extremal problems on set systems, Random Structures and Algorithms 20 (2002) 131-164, doi: 10.1002/rsa.10017.
  • [4] S. Janson, T. Łuczak and A. Ruciński, Random Graphs (Wiley, New York, 2000), doi: 10.1002/9781118032718.
  • [5] J. Komlós, G.N. Sárközy and E. Szemerédi, On the square of a Hamiltonian cycle in dense graphs, Random Structures and Algorithms 9 (1996) 193-211, doi: 10.1002/(SICI)1098-2418(199608/09)9:1/2<193::AID-RSA12>3.0.CO;2-P
  • [6] J. Komlós, G.N. Sárközy and E. Szemerédi, On the Pósa-Seymour conjecture, J. Graph Theory 29 (1998) 167-176.
  • [7] J. Polcyn, V. Rödl, A. Ruciński and E. Szemerédi, Short paths in quasi-random triple systems with sparse underlying graphs, in preparation.
  • [8] B. Nagle and V. Rödl, Regularity properties for triple systems, Random Structures and Algorithms 23 (2003) 264-332, doi: 10.1002/rsa.10094.
  • [9] V. Rödl, A. Ruciński and E. Szemerédi, A Dirac-type theorem for 3-uniform hypergraphs, submitted.
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1245
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