Alexander Souza has offered for review on arXiv a constructive solution in the affirmative.

http://arxiv.org/abs/1202.0569

Edit: Unless we are mistaken, the Petersen graph is a counterexample to Theorem 2. Furthermore there is an unresolved problem with Lemma 9.

## Claimed solution in the affirmative

Alexander Souza has offered for review on arXiv a constructive solution in the affirmative.

http://arxiv.org/abs/1202.0569

Edit: Unless we are mistaken, the Petersen graph is a counterexample to Theorem 2. Furthermore there is an unresolved problem with Lemma 9.