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2014 | 34 | 2 | 361-381
Tytuł artykułu

Families of triples with high minimum degree are hamiltonian

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we show that every family of triples, that is, a 3-uniform hypergraph, with minimum degree at least [...] contains a tight Hamiltonian cycle
Wydawca
Rocznik
Tom
34
Numer
2
Strony
361-381
Opis fizyczny
Daty
wydano
2014-05-01
online
2014-04-12
Twórcy
Bibliografia
  • [1] R. Aharoni, A. Georgakopoulos and P. Sprüssel, Perfect matchings in r-partite r- graphs, European J. Combin. 30 (2009) 39-42. doi:10.1016/j.ejc.2008.02.011[Crossref][WoS]
  • [2] E. Buss, H. H`an and M. Schacht, Minimum vertex degree conditions for loose Hamil- ton cycles in 3-uniform hypergraphs, J. Combin. Theory (B), to appear.
  • [3] R. Glebov, Y. Person andW.Weps, On extremal hypergraphs for hamiltonian cycles, European J. Combin. 33 (2012) 544-555 (An extended abstract has appeared in the Proceedings of EuroComb 2011). doi:10.1016/j.ejc.2011.10.003[Crossref]
  • [4] H. Hàn, Y. Person and M. Schacht, On perfect matchings in uniform hypergraphs with large minimum vertex degree, SIAM J. Discrete Math. 23 (2009) 732-748. doi:10.1137/080729657[Crossref][WoS]
  • [5] H. Hàn and M. Schacht, Dirac-type results for loose Hamilton cycles in uniform hypergraphs, J. Combin. Theory (B) 100 (2010) 332-346. doi:10.1016/j.jctb.2009.10.002[Crossref]
  • [6] S. Janson, T. Luczak and A. Ruci´nski, Random Graphs (John Wiley and Sons, New York, 2000). doi:10.1002/9781118032718[Crossref]
  • [7] G.Y. Katona and H.A. Kierstead, Hamiltonian chains in hypergraphs, J. Graph Theory 30 (1999) 205-212. doi:10.1002/(SICI)1097-0118(199903)30:3h205::AID-JGT5i3.0.CO;2-O[Crossref]
  • [8] P. Keevash, D. Kühn, R. Mycroft and D. Osthus, Loose Hamilton cycles in hyper- graphs, Discrete Math. 311 (2011) 544-559. doi:10.1016/j.disc.2010.11.013[Crossref]
  • [9] I. Khan, Perfect matching in 3-uniform hypergraphs with large vertex degree, SIAM J. Discrete Math. 27 (2013) 1021-1039. doi:10.1137/10080796X[Crossref][WoS]
  • [10] D. Kühn, R. Mycroft and D. Osthus, Hamilton l-cycles in uniform hypergraphs, J. ombin. Theory (A) 117 (2010) 910-927. doi:10.1016/j.jcta.2010.02.010[WoS][Crossref]
  • [11] D. Kühn and D. Osthus, Matchings in hypergraphs of large minimum degree, J. raph Theory 51 (2006) 269-280. doi:10.1002/jgt.20139[Crossref]
  • [12] D. Kühn and D. Osthus, Loose Hamilton cycles in 3-uniform hypergraphs of high minimum degree, J. Combin. Theory (B) 96 (2006) 767-821. doi:10.1016/j.jctb.2006.02.004[Crossref]
  • [13] D. Kühn, D. Osthus and A. Treglown, Matchings in 3-uniform hypergraphs, J. Com- bin. Theory (B) 103 (2013) 291-305. doi:10.1016/j.jctb.2012.11.005[Crossref]
  • [14] O. Pikhurko, Perfect matchings and K3 4 -tilings in hypergraphs of large codegree, Graphs Combin. 24 (2008) 391-404. doi:10.1007/s00373-008-0787-7[Crossref]
  • [15] V. Rödl and A. Ruciński, Dirac-type questions for hypergraphs-a survey (or more problems for Endre to solve), An Irregular Mind (Szemer´edi is 70), Bolyai Soc. Math. tud. 21 (2010) 561-590.
  • [16] V. Rödl, A. Ruciński and E. Szemer´edi, A Dirac-type theorem for 3-uniform hyper- graphs, Combin. Probab. Comput. 15 (2006) 229-251. doi:10.1017/S0963548305007042[Crossref]
  • [17] V. Rödl, A. Ruciński and E. Szemer´edi, Perfect matchings in uniform hypergraphs with large minimum degree, European. J. Combin. 27 (2006) 1333-1349. doi:10.1016/j.ejc.2006.05.008[Crossref]
  • [18] V. Rödl, A. Ruciński and E. Szemer´edi, An approximate Dirac-type theorem for k- uniform hypergraphs, Combinatorica 28 (2008) 229-260. doi:10.1007/s00493-008-2295-z[Crossref][WoS]
  • [19] V. Rödl, A. Ruciński and E. Szemer´edi, Perfect matchings in large uniform hyper- graphs with large minimum collective degree, J. Combin. Theory (A) 116 (2009) 613-636. doi:10.1016/j.jcta.2008.10.002[Crossref]
  • [20] V. Rödl, A. Ruciński and E. Szemer´edi, Dirac-type conditions for hamiltonian paths and cycles in 3-uniform hypergraphs, Adv. Math. 227 (2011) 1225-1299. doi:10.1016/j.aim.2011.03.007[WoS][Crossref]
  • [21] V. Rödl, A. Ruciński, M. Schacht and E. Szemerédi, A note on perfect matchings in uniform hypergraphs with large minimum collective degree, Comment. Math. Univ. arolin. 49 (2008) 633-636.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1743
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