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Hamilton-chain saturated hypergraphs

✍ Scribed by Aneta Dudek; Andrzej Żak; Gyula Y. Katona

Book ID
108114199
Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
415 KB
Volume
310
Category
Article
ISSN
0012-365X

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ErdGs, P., Z. Fiiredi and Z. Tuza, Saturated r-uniform hypergraphs, Discrete Mathematics 98 (1991) 95-104. The following dual version of Turin's problem is considered: for a given r-uniform hypergraph F, determine the minimum number of edges in an r-uniform hypergraph H on n vertices, such that F

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A cyclic ordering of the vertices of a k-uniform hypergraph is called a hamiltonian chain if any k consecutive vertices in the ordering form an edge. For k = 2 this is the same as a hamiltonian cycle. We consider several natural questions about the new notion. The main result is a Dirac-type theorem