Nash-Williams’ arboricity theorem states that a finite graph is the edge-disjoint union of at
most k forests if no set of ℓ vertices induces more than k(ℓ-1) edges. We prove a natural …

A theorem of Mader states that highly connected subgraphs can be forced in finite graphs
by assuming a high minimum degree. We extend this result to infinite graphs. Here, it is …

Loebl, Komlós, and Sós conjectured that if at least half of the vertices of a graph G have
degree at least some k∈N, then every tree with at most k edges is a subgraph of G. Our main …

Our topic is infinite graph theory, with our focus on the ends of an infinite graph (which can
be informally viewed as endpoints of rays), and their role in extensions of results known for …

Extremal graph theory is a branch of graph theory that seeks to explore the properties of
graphs that are in some way extreme. The classical extremal graph theoretic theorem and a …

Loebl, Komlos, and Sos conjectured that if at least half the vertices of a graph G have degree
at least some k, then every tree with at most k edges is a subgraph of G. We prove the …

… Jarett Schwartz Maya Jakobine Stein Ondrej Suchý Martin Tancer Balder ten Cate Marek
Tesar Bhalchandra Thatte Vojtech Tuma Pavel Valtr László Végh Jan Volec Geoffrey Whittle …

of doctoral thesis Structural graph theory Jan Hladký In the thesis we make progress on the
Loebl-Komlós-Sós Conjecture which is a classic problem in the field of Extremal Graph …

… Finalmente agradezco a la profesora Maya Stein, por haberme guíado en este largo pero
muy bonito proceso y con quien ha sido un privilegio trabajar este último año. Agradezco …

… Me gustaría comenzar agradeciendo a mis profesors guías Maya Stein y Hiê.p Hàn por
estos 4 años. Gracias por todo, aprendí muchísimo de ambos y guardo con mucho cariño estos …