A short proof of the versatile version of Fleischner’s theorem

We give a short proof of the following strong version of Fleischner’s theorem: if G is a 2 -connected graph and v 1 and v 2 are two distinct vertices of G , then G 2 contains a Hamiltonian cycle C such that both edges of C incident with v 1 and one further edge of C incident with v 2 belong to G .