Frankl, Péter; Katona, Gyula Y. Extremal \(k\)-edge-Hamiltonian hypergraphs. (English) Zbl 1137.05051 Discrete Math. 308, No. 8, 1415-1424 (2008). 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 \(k\). Cited in 1 ReviewCited in 11 Documents MSC: 05C65 Hypergraphs 05C45 Eulerian and Hamiltonian graphs 05C35 Extremal problems in graph theory 05D05 Extremal set theory Keywords:\(k\)-edge-Hamiltonian; Hamiltonian cycle; hypergraph PDFBibTeX XMLCite \textit{P. Frankl} and \textit{G. Y. Katona}, Discrete Math. 308, No. 8, 1415--1424 (2008; Zbl 1137.05051) 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.