# Hamiltonian cycles in powers of infinite graphs

**Conjecture**

- \item If is a countable connected graph then its third power is hamiltonian. \item If is a 2-connected countable graph then its square is hamiltonian.

(Reproduced from [M].)

Both results are known to be true for finite graphs (the second part is the celebrated result of Fleischner) and also for locally finite graphs [G].

## Bibliography

[G] A. Georgakopoulos, Oberwolfach reports, 2007.

[M] Bojan Mohar, Problem of the Month

* indicates original appearance(s) of problem.