Hamiltonian uniform subset graphs (Q1071032)

The uniform subset graph G(n,k,t) is defined to have all k-subsets of an n-set as vertices and edges joining k-subsets intersecting at t elements. The authors conjecture that G(n,k,t) is Hamiltonian when it is different from the Petersen graph and does possess cycles. We verify this conjecture for \(k-t=1,2,3\) and for suitably large n when \(t=0,1\).