Jonathan Joe

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math.CO2024

Problems on the Triangular Lattice

Gaston A. Brouwer, Jonathan Joe, Abby A. Noble +1

In this work, we consider a number of problems defined on the triangular lattice with $n$ rows, which we will denote as $T_{n}$ . Define a \textit{proper coloring} to be an assignment…

math.CO2023

A Triangle-free, 4-chromatic $Q^{3}$ Euclidean Distance Graph Scavenger Hunt!

Jonathan Joe, Matt Noble

For $d > 0$ , define $G (Q^{3}, d)$ to be the graph whose set of vertices is the rational space $Q^{3}$ , where two vertices are adjacent if and only if they are a Eucli…

Problems on the Triangular Lattice

A Triangle-free, 4-chromatic Q3 Euclidean Distance Graph Scavenger Hunt!

A Triangle-free, 4-chromatic $Q^{3}$ Euclidean Distance Graph Scavenger Hunt!