We make progress on three long standing conjectures from the 1960s about path and cycle
decompositions of graphs. Gallai conjectured that any connected graph on n vertices can be …

We consider the problem of decomposing the edges of a directed graph into as few paths as
possible. There is a natural lower bound for the number of paths needed in an edge …

We consider the problem of decomposing the edges of a digraph into as few paths as
possible. A natural lower bound for the number of paths in any path decomposition of a …

An old conjecture of Bollob\'as and Scott asserts that every Eulerian directed graph with
average degree $ d $ contains a directed cycle of length at least $\Omega (d) $. The best …

In this thesis, we make progress on five long standing conjectures on path and cycle
decompositions of graphs and digraphs. Firstly, we confirm a conjecture of Jackson from …

In this work we consider extensions of a conjecture due to Alspach, Mason, and Pullman
from 1976. This conjecture concerns edge decompositions of tournaments into as few paths …

Long Paths and Cycles in eulerian digraphs have gotten a lot of attention recently. In this
short note, we show how to use methods from Knierim, Larcher, Martinsson, Noever (2021) …

This thesis shines light on two very important topics in combinatorics: Ramsey theory and
graph decomposition problems. Studied since the beginning of the 20th century, Ramsey …

This thesis is concerned with the mathematical field of graph theory. Graphs can be used to
model many different situations or represent different types of networks (eg transport …