On extremal hypergraphs for Hamiltonian cycles

We study sufficient conditions for Hamiltonian cycles in hypergraphs, and obtain both Turan- and Dirac-type results. While the Turan-type result gives an exact threshold for the appearance of a Hamiltonian cycle in a hypergraph depending only on the extremal number of a certain path, the Dirac-type result yields a sufficient condition relying solely on the minimum vertex degree.

[1]  Vojtech Rödl,et al.  Perfect matchings in large uniform hypergraphs with large minimum collective degree , 2009, J. Comb. Theory, Ser. A.

[2]  O. Ore.  Arc coverings of graphs , 1961 .

[3]  Andrzej Rucinski,et al.  Perfect matchings (and Hamilton cycles) in hypergraphs with large degrees , 2011, Eur. J. Comb..

[4]  Vojtech Rödl,et al.  Perfect matchings in uniform hypergraphs with large minimum degree , 2006, Eur. J. Comb..

[5]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[6]  Robin Wilson,et al.  Modern Graph Theory , 2013 .

[7]  Daniela Kühn,et al.  Hamilton l-cycles in uniform hypergraphs , 2009, J. Comb. Theory, Ser. A.

[8]  Daniela Kühn,et al.  Matchings in 3-uniform hypergraphs , 2010, J. Comb. Theory, Ser. B.

[9]  Vojtech Rödl,et al.  A Dirac-Type Theorem for 3-Uniform Hypergraphs , 2006, Combinatorics, Probability and Computing.

[10]  Gyula Y. Katona,et al.  Hamiltonian chains in hypergraphs , 2006, J. Graph Theory.

[11]  Gyula Y. Katona,et al.  Hypergraph Extensions of the Erdos-Gallai Theorem , 2010, Electron. Notes Discret. Math..

[12]  Zsolt Tuza.  Steiner systems and large non-Hamiltonian hypergraphs , 2006 .

[13]  Oleg Pikhurko,et al.  Perfect Matchings and K43-Tilings in Hypergraphs of Large Codegree , 2008, Graphs Comb..

[14]  E. Szemerédi,et al.  Dirac-type conditions for hamiltonian paths and cycles in 3-uniform hypergraphs , 2011 .

[15]  E. Szemerédi,et al.  A note on perfect matchings in uniform hypergraphs with large minimum collective degree , 2008 .

[16]  Vojtech Rödl,et al.  Dirac-Type Questions For Hypergraphs — A Survey (Or More Problems For Endre To Solve) , 2010 .

[17]  Vojtech Rödl,et al.  An approximate Dirac-type theorem for k-uniform hypergraphs , 2008, Comb..

[18]  Daniela Kühn,et al.  Matchings in hypergraphs of large minimum degree , 2006, J. Graph Theory.

[19]  Hiêp Hàn,et al.  On Perfect Matchings in Uniform Hypergraphs with Large Minimum Vertex Degree , 2009, SIAM J. Discret. Math..

[20]  G. Dirac.  Some Theorems on Abstract Graphs , 1952 .

[21]  Hiêp Hàn,et al.  Dirac-type results for loose Hamilton cycles in uniform hypergraphs , 2010, J. Comb. Theory, Ser. B.

[22]  Yury Person,et al.  On Extremal Hypergraphs for Hamiltonian Cycles , 2011, Electron. Notes Discret. Math..

[23]  Ron Aharoni,et al.  Perfect matchings in r-partite r-graphs , 2009, Eur. J. Comb..