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For a loopless multigraph G, the fractional arboricity Arb(G) is the maximum of |E(H)||V(H)|−1 over all subgraphs H with at least two vertices. Generalizing the Nash-Williams Arboricity Theorem, the Nine Dragon Tree Conjecture asserts that if Arb(G)≤k+dk+d+1, then G decomposes into k+1 forests with one having maximum degree at most d. The conjecture was previously proved for d=k+1 and for k=1 when...
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