A threading path to a Ramsey number

Abstract

The article describes a collaboration between an established artist and a professional mathematician. This at the same time accidental and, in the spirit of Ramsey theory, unavoidable collaboration has resulted in creating an artwork inspired by an edge 3-colouring of the complete graph on sixteen vertices that avoids monochromatic triangles.

GRAPHICAL ABSTRACT

Keywords:

• Threading
• colouring
• monochromatic
• complete graph
• Ramsey number

Acknowledgments

The authors would like to thank Jonelle Perron for photographing Ms. Blanck's hands, Jin Cheong for documentation assistance, Karin Konstantynowicz for her help in editing Ms. Blanck's artist statement, and Dr. Daniel Král for helping us to better understand the graph-theoretical part of the project.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 See Jungić (2023).

2 The informal description of the mathematical problem that our project addresses in Section 1 is an edge 3-colouring of $K_n$, where n is the number of people in the group.

3 See Jungić (2023).

4 To grasp how huge the number $3^{120}$ is, we mention that one of its approximations is $1.8\cdot {10}^{57}$, i.e. the number that is written as eighteen followed by fifty-six zeros.

5 Investigating properties of triangle-free graphs is an important graph-theoretical task on its own merit. See West (2000).

6 We used Maple (https://www.maplesoft.com/), a symbolic and numeric computing environment and a multi-paradigm programming language, to establish this fact.

7 See Paoletti (2006).