Triangular Ramsey Numbers
Timothy Trujillo, Connor Mattes, Zachary Chaney, Jed Menard

TL;DR
This paper introduces triangular Ramsey numbers, explores their bounds, and uses a simple combinatorial game called Mines to analyze and define these numbers, providing new insights into their properties.
Contribution
It defines triangular Ramsey numbers and establishes bounds using a novel combinatorial game and probabilistic methods, expanding Ramsey theory into a new geometric context.
Findings
Triangular Ramsey numbers are introduced and bounded.
The game Mines is used to analyze triangular sets and strategies.
Lower bounds for the numbers are established using probabilistic methods.
Abstract
The purpose of this paper is to introduce the idea of triangular Ramsey numbers and provide values as well as upper and lower bounds for them. To do this, the combinatorial game Mines is introduced; after some necessary theorems about triangular sets are proved. This game is easy enough that young children are able to play. The most basic variations of this game are analyzed and theorems about winning strategies and the existence of draws are proved. The game of Mines is then used to define triangular Ramsey numbers. Lower bounds are found for these triangular Ramsey numbers using the probabilistic method and the theorems about triangular sets.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory · Advanced Graph Theory Research
