Daniel J. Poole

most citedOn Weak Hamiltonicity of a Random Hypergraph

11 citations · 11 across the 2 of their papers we have counts for

collaborators

4 papers

math.PR2016

Birth of a giant $(k_{1}, k_{2})$ -core in the random digraph

Boris Pittel, Dan Poole

The $(k_{1}, k_{2})$ -core of a digraph is the largest sub-digraph with minimum in-degree and minimum out-degree at least $k_{1}$ and $k_{2}$ respectively. For $max {k_{1}, k_{2}} \geq 2$ , we…

math.CO2014★ 11 cited

On Weak Hamiltonicity of a Random Hypergraph

Daniel Poole

A {\it weak (Berge) cycle} is an alternating sequence of vertices and (hyper)edges $C = (v_{0}, e_{1}, v_{1}, ..., v_{ℓ - 1}, e_{ℓ}, v_{ℓ} = v_{0})$ such that the vertices $v_0, ..., v_{\…

math.CO2014

On the strength of connectedness of a random hypergraph

Daniel Poole

Bollobás and Thomason (1985) proved that for each $k = k (n) \in [1, n - 1]$ , with high probability, the random graph process, where edges are added to vertex set $V = [n]$ uniformly at r…

math.PR2014

Asymptotic distribution of the numbers of vertices and arcs of the giant strong component in sparse random digraphs

Boris Pittel, Daniel Poole

Two models of a random digraph on $n$ vertices, $D (n, Prob (arc) = p)$ and $D (n, number of arcs = m)$ are studied. In 1990, Karp for $D (n, p)$ and independently T. Łuc…

Birth of a giant (k1​,k2​)-core in the random digraph

On Weak Hamiltonicity of a Random Hypergraph

On the strength of connectedness of a random hypergraph

Asymptotic distribution of the numbers of vertices and arcs of the giant strong component in sparse random digraphs

Birth of a giant $(k_{1}, k_{2})$ -core in the random digraph