Let G=(V,E)be a graph,a map φ from E(G)to { 1,2,…,t} is called a t-linear coloring if the induced subgraph of edges having the same color α is a linear forest for 1≤α≤t.The linear arboricity la(G)is the minimum number t over all t-linear coloring of G.In this paper,we determine la(G)=[Δ/2]|for graphs with maximum degree Δ and treewidth at most Δ+1/4.
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