Revisiting The Hamiltonian Theme In The Square Of A Block: The General Case

This is the second part of joint research in which we show that every 2-connected graph G has the F-4 property. That is, given distinct x(i) is an element of V(G), 1 <= i <= 4, there is an x(1)x(2)-hamiltonian path in G(2) containing different edges x(3)y(3), x(4)y(4 )is an element of E(G) for some y(3), y(4) is an element of V(G). However, it was shown already in [3, Theorem 2] that 2-connected DT-graphs have the F-4 property; based on this result we generalize it to arbitrary 2-connected graphs. We also show that these results are best possible.