Listing spanning trees of outerplanar graphs by pivot exchanges
<|reference_start|>Listing spanning trees of outerplanar graphs by pivot exchanges: We prove that the spanning trees of any outerplanar triangulation $G$ can be listed so that any two consecutive spanning trees differ in an exchange of two edges that share an end vertex. For outerplanar graphs $G$ with faces of arbitrary lengths (not necessarily 3) we establish a similar result, with the condition that the two exchanged edges share an end vertex or lie on a common face. These listings of spanning trees are obtained from a simple greedy algorithm that can be implemented efficiently, i.e., in time $\mathcal{O}(n \log n)$ per generated spanning tree, where $n$ is the number of vertices of $G$. Furthermore, the listings correspond to Hamilton paths on the 0/1-polytope that is obtained as the convex hull of the characteristic vectors of all spanning trees of $G$.<|reference_end|>
@article{behrooznia2024listing,
    title={Listing spanning trees of outerplanar graphs by pivot exchanges},
    author={Nastaran Behrooznia, Torsten M"utze},
    journal={arXiv preprint arXiv:2409.15793},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.15793},
    primaryClass={cs.DM math.CO}
}