3 citations · 6 across the 10 of their papers we have counts for
10 papers · 1 filter
The Toucher-Isolator game
Chris Dowden, Mihyun Kang, Mirjana Mikalački +1
We introduce a new positional game called `Toucher-Isolator', which is a quantitative version of a Maker-Breaker type game. The playing board is the set of edges of a given graph G…
The genus of the Erdős-Rényi random graph and the fragile genus property
Chris Dowden, Mihyun Kang, Michael Krivelevich
We investigate the genus of the Erdős-Rényi random graph , providing a thorough description of how this relates to the function , and finding that there is…
The evolution of random graphs on surfaces
Chris Dowden, Mihyun Kang, Philipp Sprüssel
For integers and , let denote the graph taken uniformly at random from the set of all graphs on with exactly edges and…
Extremal C4-free/C5-free planar graphs
Chris Dowden
We study the topic of "extremal" planar graphs, defining to be the maximum number of edges possible in a planar graph on vertices that does…
Uniform Random Planar Graphs with Degree Constraints
Chris Dowden
Random planar graphs have been the subject of much recent work. Many basic properties of the standard uniform random planar graph P_{n}, by which we mean a graph chosen uniformly a…
On the maximum size of minimal definitive quartet sets
Chris Dowden
In this paper, we investigate a problem concerning quartets, which are a particular type of tree on four leaves. Loosely speaking, a set of quartets is said to be `definitive' if i…