3 citations · 6 across the 10 of their papers we have counts for
5 papers · 2 filters
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…
Subgraphs of 4-regular planar graphs
Chris Dowden, Louigi Addario-Berry
We shall present an algorithm for determining whether or not a given planar graph H can ever be a subgraph of a 4-regular planar graph. The algorithm has running time O(|H|^{2.5})…
Random planar graphs with bounds on the maximum and minimum degrees
Chris Dowden
Let P_{n,d,D} denote the graph taken uniformly at random from the set of all labelled planar graphs on {1,2,...,n} with minimum degree at least d(n) and maximum degree at most D(n)…
The evolution of uniform random planar graphs
Chris Dowden
Let P_{n,m} denote the graph taken uniformly at random from the set of all planar graphs on {1,2,..., n} with exactly m(n) edges. We use counting arguments to investigate the proba…
An axiomatic approach to diversity
Chris Dowden
The topic of diversity is an interesting subject, both as a purely mathematical concept and also for its applications to important real-life situations. Unfortunately, although the…