# Hamilton decomposition of prisms over 3-connected cubic planar graphs

**Conjecture**Every prism over a -connected cubic planar graph can be decomposed into two Hamilton cycles.

The *prism over* a graph is the Cartesian product .

Rosenfeld and Barnette [RB] deduced from the Four-Colour Theorem that the prism over cubic planar 3-connected has a Hamilton cycle . The graph is cycle factor (spanning union of cycles). The conjecture says that one can choses so that the cycle factor has a unique cycle, that is a Hamilton cycle.

## Bibliography

*[AR] B. Alspach and M. Rosenfeld, On Hamilton decompositions of prisms over simple -polytopes. Graphs Combin. 2 (1986), 1--8.

[RB] M. Rosenfeld and D. Barnette, Hamiltonian circuits in certain prisms, Discrete Math. 5 (1973) 389–394.

* indicates original appearance(s) of problem.