Minimum degree ensuring that a hypergraph is Hamiltonian-connected
Abstract: A hypergraph H is Hamiltonian-connected if for any distinct vertices x and y, H contains a Hamiltonian Berge path from x to y. We find for all 3\leq r<n, exact lower bounds on minimum degree \delta(n,r) of an n-vertex r-uniform hypergraph H guaranteeing that H is Hamiltonian-connected. It turns out that for 3\leq n/2<r<n, \delta(n,r) is 1 less than the degree bound guaranteeing the existence of a Hamiltonian Berge cycle.
