Austin Eide

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4 papers · 1 filter

math.CO2025

Multiset Metric Dimension of Binomial Random Graphs

Austin Eide, Pawel Pralat

For a graph $G = (V, E)$ and a subset $R \subseteq V$ , we say that $R$ is \textit{multiset resolving} for $G$ if for every pair of vertices $v, w$ , the \textit{multisets} $\{d(v,r):…

math.CO2025

Playing Sudoku on random 3-regular graphs

Jack Dippel, Austin Eide, Pawel Pralat +1

The Sudoku number $s (G)$ of graph $G$ with chromatic number $χ (G)$ is the smallest partial $χ (G)$ -colouring of $G$ that determines a unique $χ (G)$ -colouring of the entire graph. We…

math.CO2024

Burning Random Trees

Luc Devroye, Austin Eide, Pawel Pralat

Let $T$ be a Galton-Watson tree with a given offspring distribution $ξ$ , where $ξ$ is a $Z_{\geq 0}$ -valued random variable with $E [ξ] = 1$ and $0 < σ^{2}:=Var[ξ] < \inft…

math.CO2023

Linear Colouring of Binomial Random Graphs

Austin Eide, Paweł Prałat

We investigate the linear chromatic number $χ_{lin} (G (n, p))$ of the binomial random graph $G (n, p)$ on $n$ vertices in which each edge appears independently with probability…