Short paths in 3-uniform quasi-random hypergraphs

• Autorzy: Joanna Polcyn
• 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

EN

hypergraph; path; quasi-randomness

Kategorie tematyczne

• 05C12: Distance in graphs
• 05C38: Paths and cycles
• 05C65: Hypergraphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2004
• Tom: 24
• Numer: 3
• Strony: 469-484

Daty

wydano

2004

otrzymano

2003-06-18

poprawiono

2004-01-21

Twórcy

autor

Joanna Polcyn

• 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.

Identyfikatory

DOI

10.7151/dmgt.1245