Families of triples with high minimum degree are hamiltonian
Vojtech Rödl ; Andrzej Ruciński
Discussiones Mathematicae Graph Theory, Tome 34 (2014), p. 361-381 / Harvested from The Polish Digital Mathematics Library

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

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:267869
@article{bwmeta1.element.doi-10_7151_dmgt_1743,
     author = {Vojtech R\"odl and Andrzej Ruci\'nski},
     title = {Families of triples with high minimum degree are hamiltonian},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {34},
     year = {2014},
     pages = {361-381},
     zbl = {1290.05114},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1743}
}
Vojtech Rödl; Andrzej Ruciński. Families of triples with high minimum degree are hamiltonian. Discussiones Mathematicae Graph Theory, Tome 34 (2014) pp. 361-381. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1743/

[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] | Zbl 1204.05072

[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. | Zbl 1274.05335

[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] | Zbl 1237.05142

[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] | Zbl 1191.05074

[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] | Zbl 1209.05161

[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] | Zbl 0924.05050

[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] | Zbl 1226.05187

[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] | Zbl 1272.05160

[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] | Zbl 1219.05107

[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] | Zbl 1087.05041

[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] | Zbl 1109.05065

[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] | Zbl 1262.05128

[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] | Zbl 1205.05184

[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. | Zbl 1221.05255

[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] | Zbl 1104.05051

[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] | Zbl 1164.05051

[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. | Zbl 1212.05215