A note on the edge partition of graphs containing either a light edge or an alternating 2-cycle
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Let G_α be a hereditary graph class (i.e, every subgraph of G_α∈G_α belongs to G_α) such that every graph G_α in G_α has minimum degree at most 1, or contains either an edge uv such that d_G_α(u)+d_G_α(v)≤α or a 2-alternating cycle. It is proved that every graph in G_α (α≥ 5) with maximum degree Δ can be edge-partitioned into two forests F_1, F_2 and a subgraph H such that Δ(F_i)≤{2,Δ-α+6/2} for i=1,2 and Δ(H)≤α-5.
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