6-cycle double covers of cubic graphs
<|reference_start|>6-cycle double covers of cubic graphs: A cycle double cover (CDC) of an undirected graph is a collection of the graph's cycles such that every edge of the graph belongs to exactly two cycles. We describe a constructive method for generating all the cubic graphs that have a 6-CDC (a CDC in which every cycle has length 6). As an application of the method, we prove that all such graphs have a Hamiltonian cycle. A sense of direction is an edge labeling on graphs that follows a globally consistent scheme and is known to considerably reduce the complexity of several distributed problems. In [9], a particular instance of sense of direction, called a chordal sense of direction (CSD), is studied and the class of k-regular graphs that admit a CSD with exactly k labels (a minimal CSD) is analyzed. We now show that nearly all the cubic graphs in this class have a 6-CDC, the only exception being K4.<|reference_end|>
@article{leao20056-cycle,
    title={6-cycle double covers of cubic graphs},
    author={Rodrigo S. C. Leao, Valmir C. Barbosa},
    journal={arXiv preprint arXiv:cs/0505088},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0505088},
    primaryClass={cs.DM}
}