Austin Eide
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View article: Direct Paths in the Temporal Hypercube
Direct Paths in the Temporal Hypercube Open
We consider the $n$-dimensional random temporal hypercube, i.e., the $n$-dimensional hypercube graph with its edges endowed with i.i.d. continuous random weights. We say that a vertex $w$ is accessible from another vertex $v$ if and only i…
View article: Multiset Metric Dimension of Binomial Random Graphs
Multiset Metric Dimension of Binomial Random Graphs Open
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} $\{d(v,r): r \in R\}$ and $\{d(w,r):r \in R\}$ are distinct, where $d(…
View article: Concentration and central limit theorem for the averaging process on $\mathbb{Z}^{d}$
Concentration and central limit theorem for the averaging process on $\mathbb{Z}^{d}$ Open
In the averaging process on a graph $G = (V, E)$, a random mass distribution $η$ on $V$ is repeatedly updated via transformations of the form $η_{v}, η_{w} \mapsto (η_{v} + η_{w})/2$, with updates made according to independent Poisson cloc…
View article: Linear Colouring of Binomial Random Graphs
Linear Colouring of Binomial Random Graphs Open
We investigate the linear chromatic number $χ_{\text{lin}}(G(n,p))$ of the binomial random graph $G(n,p)$ on $n$ vertices in which each edge appears independently with probability $p=p(n)$. For dense random graphs ($np \to \infty$ as $n \t…