This note summarizes the state of what is known about the tractability of the problem
ModPath, which asks if an input undirected graph contains a simple st-path whose length …

We prove the existence of a computable function f∶ ℕ→ ℕ such that for every integer k and
every digraph D, either D contains a collection C of k directed cycles of even length such that …

For a group $\Gamma $, a $\Gamma $-labelled graph is an undirected graph $ G $ where
every orientation of an edge is assigned an element of $\Gamma $ so that opposite …

In 1965, Erd\H {o} s and P\'{o} sa proved that there is a duality between the maximum size of
a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality …

In this paper, we consider a variant of dichromatic number on digraphs with prescribed sets
of arcs. Let $ D $ be a digraph and let $ Z_1, Z_2 $ be two sets of arcs in $ D $. For a …

Consider a matroid $ M $ whose ground set is equipped with a labeling to an abelian group.
A basis of $ M $ is called $ F $-avoiding if the sum of the labels of its elements is not in a …

We prove a refinement of the flat wall theorem of Robertson and Seymour to undirected
group-labelled graphs (G, γ) where γ assigns to each edge of an undirected graph G an …

We prove that there exists a function f: ℕ→ ℝ such that every directed graph G contains
either k directed odd cycles where every vertex of G is contained in at most two of them, or a …

We characterize the obstructions to the Erd\H {o} sP\'osa property of $ A $-paths in
unoriented group-labelled graphs. As a result, we prove that for every finite abelian group …

This thesis concerns itself with two related topics: First, we discuss how the relatively
esoteric area of structural matching theory can be used to solve problems in more …