English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

For a loopless multigraph $G$, the fractional arboricity $Arb(G)$ is themaximum of $\frac{|E(H)|}{|V(H)|-1}$ over all subgraphs $H$ with at least twovertices. Generalizing the Nash-Williams Arboricity Theorem, the Nine DragonTree Conjecture asserts that if $Arb(G)\le k+\frac{d}{k+d+1}$, then $G$decomposes into $k+1$ forests with one having maximum degree at most $d$. Theconjecture was previously proved for $d=k+1$ and for $k=1$ when $d \le 6$. Weprove it for all $d$ when $k \le 2$, except for $(k,d)=(2,1)$.

Decomposition of Sparse Graphs into Forests: The Nine Dragon Tree Conjecture for $k \le 2$