Hamiltonicity and pancyclicity of cartesian products of graphs

The cartesian product of a graph G with K"2 is called a prism over G. We extend known conditions for hamiltonicity and pancyclicity of the prism over a graph G to the cartesian product of G with paths, cycles, cliques and general graphs. In particular we give results involving cubic graphs and almost claw-free graphs. We also prove the following: Let G and H be two connected graphs. Let both G and H have a 2-factor. If @D(G)@?g^'(H) and @D(H)@?g^'(G) (we denote by g^'(F) the length of a shortest cycle in a 2-factor of a graph F taken over all 2-factorization of F), then [email protected]?H is hamiltonian.

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