In this paper, we study the relationship between spectral radius and maximum average
degree of graphs. By using this relationship and the previous technique of Li and Ning in (J …

The arboricity Γ (G) of an undirected graph G=(V, E) is the minimal number k such that E can
be partitioned into k forests. Nash–Williams' formula states that k=⌈ γ (G)⌉, where γ (G) is …

A graph $ G $ is said to be Ramsey for a tuple of graphs $(H_1,\dots, H_r) $ if every $ r $-
coloring of the edges of $ G $ contains a monochromatic copy of $ H_i $ in color $ i $, for …

The pseudoforest version of the Strong Nine Dragon Tree Conjecture states that if a graph $
G $ has maximum average degree $\text {mad}(G)= 2\max_ {H\subseteq G}\frac {e (G)}{v …

The maximum average degree $\mathrm {mad}(G) $ of a graph $ G $ is the maximum
average degree over all subgraphs of $ G $. In this paper we prove that for every $ G $ and …

The fractional arboricity of a digraph DD, denoted by γ (D) γ(D), is defined as γ (D)= max H⊆
D,| V (H)|> 1| A (H)|| V (H)|− 1 γ(D)=\maxH⊆D,|V(H)|\gt1|A(H)||V(H)|-1. Frank proved that a …

We prove the Strong Nine Dragon Tree Conjecture is true if we replace $ d $ with $ d+\frac
{k}{2}\cdot (\big\lceil {\frac {d}{k+ 1}}\big\rceil-1)\big\lceil {\frac {d}{k+ 1}}\big\rceil $. More …

In this thesis, we investigate arboricity and transversal problems on graphs in a bounded
degree setting. We pay particular attention to problems involving both the maximum degree …

This dissertation will be based on results from structural graph theory, mainly revolving
around graph width parameters, dependencies between them, their usages and finding …

Chen, Kim, Kostochka, West, and Zhu conjectured a strengthening of the Nine Dragon Tree
Theorem that every graph that is (k, d)-sparse and has no overfull set decomposes into k+ 1 …