The vertex set of any simple graph admits an equitable partition into k induced linear forests for every k at least max of ceil((Δ(G)+1)/2) and ceil(|G|/4).
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Equitable partition of graphs into induced linear forests
The vertex set of any simple graph admits an equitable partition into k induced linear forests for every k at least max of ceil((Δ(G)+1)/2) and ceil(|G|/4).