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 that provides a sufficient condition for finding hamiltonian chains in k-uniform hypergraphs with large (k − 1)-minimal degree. If it is more than than the hypergraph contains a hamiltonian chain.
No takes yet. Share an insight, caveat, or question.
Katona et al. (1999) studied this question.