The Strong Nine Dragon Tree Conjecture is True for
S Mies, B Moore - Combinatorica, 2023 - Springer
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 …
be partitioned into k forests. Nash–Williams' formula states that k=⌈ γ (G)⌉, where γ (G) is …
Resolution of the Kohayakawa-Kreuter conjecture
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 …
coloring of the edges of $ G $ contains a monochromatic copy of $ H_i $ in color $ i $, for …
An Approximate Version of the Strong Nine Dragon Tree Conjecture
S Mies, B Moore - arXiv preprint arXiv:2406.05022, 2024 - arxiv.org
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 …
{k}{2}\cdot (\big\lceil {\frac {d}{k+ 1}}\big\rceil-1)\big\lceil {\frac {d}{k+ 1}}\big\rceil $. More …