Shortest Path Separators in Unit Disk Graphs
<|reference_start|>Shortest Path Separators in Unit Disk Graphs: We introduce a new balanced separator theorem for unit-disk graphs involving two shortest paths combined with the 1-hop neighbours of those paths and two other vertices. This answers an open problem of Yan, Xiang and Dragan [CGTA '12] and improves their result that requires removing the 3-hop neighborhood of two shortest paths. Our proof uses very different ideas, including Delaunay triangulations and a generalization of the celebrated balanced separator theorem of Lipton and Tarjan [J. Appl. Math. '79] to systems of non-intersecting paths.<|reference_end|>
@article{harb2024shortest,
    title={Shortest Path Separators in Unit Disk Graphs},
    author={Elfarouk Harb and Zhengcheng Huang and Da Wei Zheng},
    journal={arXiv preprint arXiv:2407.15980},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.15980},
    primaryClass={cs.CG cs.DS}
}