Michael Missethan

activity

20202024

most citedLongest and shortest cycles in random planar graphs

3 citations · 4 across the 9 of their papers we have counts for

collaborators

9 papers

math.CO2024

Bootstrap percolation on the high-dimensional Hamming graph

Mihyun Kang, Michael Missethan, Dominik Schmid

In the random $r$ -neighbour bootstrap percolation process on a graph $G$ , a set of initially infected vertices is chosen at random by retaining each vertex of $G$ independently wit…

math.CO2022★ 1 cited

The emergence of a giant rainbow component

Oliver Cooley, Tuan Anh Do, Joshua Erde +1

The random coloured graph $G_{c} (n, p)$ is obtained from the Erdős-Rényi binomial random graph $G (n, p)$ by assigning to each edge a colour from a set of $c$ colours independently and…

math.CO2021

The early evolution of the random graph process in planar graphs and related classes

Mihyun Kang, Michael Missethan

We study the random planar graph process introduced by Gerke, Schlatter, Steger, and Taraz [The random planar graph process, Random Structures Algorithms 32 (2008), no. 2, 236--261…

math.CO2021

Component behaviour and excess of random bipartite graphs near the critical point

Tuan Anh Do, Joshua Erde, Mihyun Kang +1

The binomial random bipartite graph $G (n, n, p)$ is the random graph formed by taking two partition classes of size $n$ and including each edge between them independently with probab…

math.CO2021

Concentration of maximum degree in random planar graphs

Mihyun Kang, Michael Missethan

Let $P (n, m)$ be a graph chosen uniformly at random from the class of all planar graphs on vertex set $[n] := {1, \dots, n}$ with $m = m (n)$ edges. We show that in the spa…

math.CO2021

Local limit of sparse random planar graphs

Mihyun Kang, Michael Missethan

Let $P (n, m)$ be a graph chosen uniformly at random from the class of all planar graphs on vertex set ${1, \dots, n}$ with $m = m (n)$ edges. We determine the (Benjamini-…

math.CO2020

Two point concentration of maximum degree in sparse random planar graphs

Mihyun Kang, Michael Missethan

Let $P (n, m)$ be a graph chosen uniformly at random from the class of all planar graphs on vertex set ${1, \dots, n}$ with $m = m (n)$ edges. We show that in the sparse r…

math.CO2020★ 3 cited

Longest and shortest cycles in random planar graphs

Mihyun Kang, Michael Missethan

Let $P (n, m)$ be a graph chosen uniformly at random from the class of all planar graphs on vertex set ${1, \dots, n}$ with $m = m (n)$ edges. We study the cycle and block structure…

math.CO2020

The giant component and 2-core in sparse random outerplanar graphs

Mihyun Kang, Michael Missethan

Let $A (n, m)$ be a graph chosen uniformly at random from the class of all vertex-labelled outerplanar graphs with $n$ vertices and $m$ edges. We consider $A (n, m)$ in the sparse regi…