@article{Lai2001HamiltonWA,
title={Hamilton weights and Petersen minors},
author={Hong-Jian Lai and Cun-Quan Zhang},
journal={Journal of Graph Theory},
year={2001},
volume={38},
pages={197-219}
}

A (1, 2)-eulerian weight w of a cubic graph is called a Hamilton weight if every faithful circuit cover of the graph with respect to w is a set of two Hamilton circuits. Let G be a 3-connected cubic graph containing no Petersen minor. It is proved in this paper that G admits a Hamilton weight if and only if G can be obtained from K4 by a series of4$Y-operations. As a byproduct of the proof of the main theorem, we also prove that if G is a permutation graph and w is a (1,2)-eulerian weight of G… CONTINUE READING