In this thesis we consider two classes of binary matroids, even cycle matroids and even cut matroids. They are a generalization of graphic and cographic matroids respectively. We focus on two main… Expand

A biased graph consists of a graph G together with a collection of distinguished cycles of G, called balanced, with the property that no theta subgraph contains exactly two balanced cycles.Expand

We characterise the structure of graphs with no two vertex-disjoint unbalanced cycles, answering a question by Zaslavsky and generalising the results of Lovasz and Slilaty.Expand

Let T be a distinguished subset of vertices in a graph G. A T-Steiner tree is a subgraph of G that is a tree and that spans T. Kriesell conjectured that G contains k pairwise edge-disjoint T-Steiner… Expand

In this paper we consider the number of Hamilton cycles in planar cubic graphs of high cyclic edge-connectivity, answering two questions raised by Chia and Thomassen about extremal graphs in these families.Expand

Climate change has a strong impact on marine ecosystems, including temperate species. Analysing the diversity of thermotolerance levels within species along with their genetic structure enables a… Expand

We prove that the maximum size of a simple binary matroid of rank $r \geq 5$ with no $AG(3,2)$-minor is $\binom{r+1}{2}$ and characterize those matroids achieving this bound.Expand