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arXiv · 2209.01190

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

Oswin Aichholzer·Alfredo García·Irene Parada·Birgit Vogtenhuber·Alexandra Weinberger
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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 $K_{m,n}$ contains a plane spanning tree as a subdrawing. We answer this question to the positive by showing that for every simple drawing of $K_{m,n}$ 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 $v$.

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Oswin Aichholzer, Alfredo García, Irene Parada, Birgit Vogtenhuber, Alexandra Weinberger. 2022-09-02. Shooting Stars in Simple Drawings of $K_{m,n}$. https://arxiv.org/abs/2209.01190

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