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arXiv · 1812.02866

Non-crossing geometric spanning trees with bounded degree and monochromatic leaves on bicolored point sets

Mikio Kano·Kenta Noguchi·David Orden
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Abstract

Let $R$ and $B$ be a set of red points and a set of blue points in the plane, respectively, such that $R\cup B$ is in general position, and let $f:R \to \{2,3,4, \ldots \}$ be a function. We show that if $2\le |B|\le \sum_{x\in R}(f(x)-2) + 2$, then there exists a non-crossing geometric spanning tree $T$ on $R\cup B$ such that $2\le \operatorname{deg}_T(x)\le f(x)$ for every $x\in R$ and the set of leaves of $T$ is $B$, where every edge of $T$ is a straight-line segment.

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Mikio Kano, Kenta Noguchi, David Orden. 2018-12-07. Non-crossing geometric spanning trees with bounded degree and monochromatic leaves on bicolored point sets. https://arxiv.org/abs/1812.02866

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