Let $P$ be a set of $n\geq 4$ points in general position in the plane. Consider all the closed straight line segments with both endpoints in $P$. Suppose that these segments are colored with the rule that disjoint segments receive different colors. In this paper we show that if $P$ is the point configuration known as the double chain, with $k$ points in the upper convex chain and $l \ge k$ points in the lower convex chain, then $k+l- \left\lfloor \sqrt{2l+\frac{1}{4}} - \frac{1}{2}\right\rfloor$ colors are needed and that this number is sufficient.

Source : oai:arXiv.org:1711.05425

Volume: vol. 22 no. 1

Section: Graph Theory

Published on: March 22, 2020

Submitted on: May 9, 2018

Keywords: Mathematics - Combinatorics

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