Fabila-Monroy, Ruy and Hidalgo-Toscano, Carlos and Leaños, Jesús and Lomelí-Haro, Mario - The Chromatic Number of the Disjointness Graph of the Double Chain

dmtcs:4490 - Discrete Mathematics & Theoretical Computer Science, March 22, 2020, vol. 22 no. 1
The Chromatic Number of the Disjointness Graph of the Double Chain

Authors: Fabila-Monroy, Ruy and Hidalgo-Toscano, Carlos and Leaños, Jesús and Lomelí-Haro, Mario

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.


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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