Hajós conjectured in 1968 that every Eulerian n-vertex graph can be decomposed into at
most⌊(n− 1)/2⌋ edge-disjoint cycles. This has been confirmed for some special graph …

Hajós' conjecture asserts that a simple Eulerian graph on n vertices can be decomposed
into at most⌊(n− 1)/2⌋ cycles. The conjecture is only proved for graph classes in which …

The book Graph Theory and Decomposition covers major areas of the decomposition of
graphs. It is a three-part reference book with nine chapters that is aimed at enthusiasts as …

Gallai (1966) conjectured that the edge set of every graph G on n vertices can be covered by
at most⌈ n/2⌉ edge-disjoint paths. Such a covering by edge-disjoint paths is called a path …

These notes cover the first two semesters of graph theory along with more advanced topics.
These notes have been used as course notes multiple times for graph theory offerings at …

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 …

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 …

The thesis is divided into two parts. The first part deals with t-perfect graphs. A graph is
called t-perfect if its stable set polytope is fully described by non-negativity, edge and odd …

La deuxième famille de coloration consiste à colorer les arêtes au lieu des sommets en
respectant différents critères. Nous étudions quatre types de colorations d'arêtes: la …

In this thesis we study various problems from the prominent area of graph colourings. We
provide a characterisation of t-perfect triangulations and quadrangulations of the projective …