English

Shooting Stars in Simple Drawings of $K_{m,n}$

Computational Geometry 2022-09-05 v1 Combinatorics

Abstract

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,nK_{m,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,nK_{m,n} and for every vertex vv in that drawing, the drawing contains a shooting star rooted at vv, that is, a plane spanning tree containing all edges incident to vv.

Keywords

Cite

@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)