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On hamiltonian chain saturated uniform hypergraphs

Abstract : We say that a hypergraph H is hamiltonian chain saturated if H does not contain a hamiltonian chain but by adding any new edge we create a hamiltonian chain in H. In this paper we ask about the smallest size of a k-uniform hamiltonian chain saturated hypergraph. We present a construction of a family of k-uniform hamiltonian chain saturated hypergraphs with O(n(k-1/2)) edges.
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Aneta Dudek, Andrzej Zak. On hamiltonian chain saturated uniform hypergraphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2012, Vol. 14 no. 1 (1), pp.21-28. ⟨hal-00990568⟩

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