Free Sets in Planar Graphs: History and Applications
<|reference_start|>Free Sets in Planar Graphs: History and Applications: A subset $S$ of vertices in a planar graph $G$ is a free set if, for every set $P$ of $|S|$ points in the plane, there exists a straight-line crossing-free drawing of $G$ in which vertices of $S$ are mapped to distinct points in $P$. In this survey, we review   - several equivalent definitions of free sets, - results on the existence of large free sets in planar graphs and subclasses of planar graphs, - and applications of free sets in graph drawing.   The survey concludes with a list of open problems in this still very active research area.<|reference_end|>
@article{dujmovic2024free,
    title={Free Sets in Planar Graphs: History and Applications},
    author={Vida Dujmovic and Pat Morin},
    journal={arXiv preprint arXiv:2403.17090},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.17090},
    primaryClass={cs.CG cs.DM math.CO}
}