Every d-degenerate graph with maximum degree Δ ≥ 9.818d admits an equitable tree-k-coloring for every integer k ≥ (Δ+1)/2, confirming the Equitable Vertex Arboricity Conjecture for low-degeneracy graphs.
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Equitable vertex arboricity conjecture holds for graphs with low degeneracy
Every d-degenerate graph with maximum degree Δ ≥ 9.818d admits an equitable tree-k-coloring for every integer k ≥ (Δ+1)/2, confirming the Equitable Vertex Arboricity Conjecture for low-degeneracy graphs.