Current students

Title: Acyclic Colouring of Graphs on Surfaces

Abstract: An acyclic k-colouring of a graph G is a proper k-colouring of G with no

Title: Using Linear Algebra to do Matching Theory

Abstract:

A matching in a graph is a set of edges with each vertex contained in at most one edge. A perfect matching is a matching in which each vertex is contained in some edge.

Title: Density and Structure of Homomorphism-Critical Graphs

Abstract: 

Let H be a graph. A graph G is H-critical if every proper subgraph of G admits a homomor-
phism to H, but G itself does not.

Title: Claw-free matroids

Abstract: A simple binary matroid is claw-free if it has no independent rank-3 flat. I will discuss a structure theorem, obtained jointly with Kazuhiro Nomoto, that classifies these objects exactly.

Title: Algorithms for Rank-1 Bimatrix Games

Abstract:

The rank of a bimatrix game is the matrix rank of the sum of the two payoff matrices.

Title: The geometry of matroids

Abstract:

Matroid theory is a combinatorial theory of independence which has its origins in linear algebra and graph theory, and turns out to have deep connections with many other fields.

Title: Periodicity on Oriented Graphs by way of Transcendental Number Theory

Abstract: Using the adjacency matrix of a graph, it is straightforward to show that perfect state transfer between two vertices at some time t implies that both vertices will be periodic at time 2t.

Title: Gaps in the crossing numbers of drawings of the complete graph

Abstract: In the late 1990’s, a 5-author manuscript circulated proving the existence of intervals of integers that connot occur as the crossing number of a “good” drawing of the complete graph. 

Title:Generalizing the problem of packing disjoint cycles

Abstract: A classic result of Erdos and Posa states that there exists a function f such that for all k,

Title: Edge State Transfer

Abstract: Most research about quantum state transfer on graphs use adjacency matrices as their Hamiltonians and investigate the transfers between single vertex states.