Simple drawings are drawings of graphs in which two edges have at most one common point (either a common endpoint, or a proper crossing). It has been an open question whether every simple drawing of a complete bipartite graph Km,n contains a plane spanning tree as a subdrawing. We answer this question to the positive by showing that for every simple drawing of Km,n and for every vertex v in that drawing, the drawing contains a shooting star rooted at v, that is, a plane spanning tree containing all edges incident to v.
@article{arxiv.2209.01190,
title = {Shooting Stars in Simple Drawings of $K_{m,n}$},
author = {Oswin Aichholzer and Alfredo García and Irene Parada and Birgit Vogtenhuber and Alexandra Weinberger},
journal= {arXiv preprint arXiv:2209.01190},
year = {2022}
}
Comments
Appears in the Proceedings of the 30th International Symposium on Graph Drawing and Network Visualization (GD 2022)