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Extremal \(k\)-edge-Hamiltonian hypergraphs. (English) Zbl 1137.05051

Summary: An \(r\)-uniform hypergraph is \(k\)-edge-Hamiltonian if and only if it still contains a Hamiltonian-chain after deleting any \(k\) edges of the hypergraph. What is the minimum number of edges in such a hypergraph? We give lower and upper bounds for this question for several values of \(r\) and \(k\).

MSC:

05C65 Hypergraphs
05C45 Eulerian and Hamiltonian graphs
05C35 Extremal problems in graph theory
05D05 Extremal set theory
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Full Text: DOI

Online Encyclopedia of Integer Sequences:

Minimal number of edges in an n-stable graph.

References:

[1] Katona, G. Y.; Kierstead, H. A., Hamiltonian chains in hypergraphs, J. Graph Theory, 30, 3, 205-212 (1999) · Zbl 0924.05050
[2] Paoli, M.; Wong, W. W.; Wong, C. K., Minimum \(k\)-hamiltonian graphs. II, J. Graph Theory, 10, 1, 79-95 (1986) · Zbl 0592.05043
[3] Tuza, Z., Steiner systems and large non-hamiltonian hypergraphs, Matematiche (Catania), 61, 173-180 (2006)
[4] Wong, W. W.; Wong, C. K., Minimum \(k\)-hamiltonian graphs, J. Graph Theory, 8, 1, 155-165 (1984) · Zbl 0534.05040
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