论文信息 - Hypergraph Extensions of the Erdos-Gallai Theorem

Hypergraph Extensions of the Erdos-Gallai Theorem

Abstract The Erdős-Gallai Theorem gives the maximum number of edges in a graph without a path of length k. We extend this result for Berge paths in r-uniform hypergraphs. We also find the extremal hypergraphs avoiding t-tight paths of a given length and consider this extremal problem for other definitions of paths in hypergraphs.

Gyula Y. Katona | Ervin Györi | Nathan Lemons

[1] Zoltán Füredi,et al. Exact solution of some Turán-type problems , 1987, J. Comb. Theory, Ser. A.

[2] Peter Frankl,et al. Extremal k-edge-hamiltonian Hypergraphs , 2001, Electron. Notes Discret. Math..

[3] Vojtech Rödl,et al. On a Packing and Covering Problem , 1985, Eur. J. Comb..

[4] Balazs Patkos,et al. A note on traces of set families , 2011, 1111.4636.

[5] Jacques Verstraëte,et al. Minimal paths and cycles in set systems , 2007, Eur. J. Comb..

[6] Zoltán Füredi. Linear paths and trees in uniform hypergraphs , 2011, Electron. Notes Discret. Math..

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

[8] Yury Person,et al. On extremal hypergraphs for Hamiltonian cycles , 2011, Eur. J. Comb..

[9] P. Erdos,et al. On maximal paths and circuits of graphs , 1959 .

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

[11] Gyula Y. Katona,et al. Generating quadrangulations of surfaces with minimum degree at least 3 , 1999 .

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

[13] Sylvain Gravier,et al. Monochromatic Hamiltonian t-tight Berge-cycles in hypergraphs , 2008, J. Graph Theory.

[14] Sylvain Gravier,et al. Monochromatic Hamiltonian t-tight Berge-cycles in hypergraphs , 2008 .