Matt Noble

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20212024

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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…

math.CO2021

Embedding Euclidean Distance Graphs in $R^{n}$ and $Q^{n}$

Matt Noble

For $S \subseteq R$ , positive integer $n$ , and $d > 0$ , let $G (S^{n}, d)$ be the graph whose vertex set is $S^{n}$ where any two vertices are adjacent if and only if they are…

math.CO2021

On Rainbow Cycles and Proper Edge Colorings of Generalized Polygons

Matt Noble

An edge coloring of a simple graph $G$ is said to be \textit{proper rainbow-cycle-forbidding} (PRCF, for short) if no two incident edges receive the same color and for any cycle in…

math.CO2021

Answer to an Isomorphism Problem in $Z^{2}$

Matt Noble

For $S \subset R^{n}$ and $d > 0$ , denote by $G (S, d)$ the graph with vertex set $S$ with any two vertices being adjacent if and only if they are at a Euclidean distance $d$ …

Problems on the Triangular Lattice

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

Embedding Euclidean Distance Graphs in Rn and Qn

On Rainbow Cycles and Proper Edge Colorings of Generalized Polygons

Answer to an Isomorphism Problem in Z2

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

Embedding Euclidean Distance Graphs in $R^{n}$ and $Q^{n}$

Answer to an Isomorphism Problem in $Z^{2}$