On the path partition of graphs
Let G be a graph of order n. The maximum and minimum degree of G are denoted by Δ and δ respectively. The path partition number μ (G) of a graph G is the minimum number of paths needed to partition the vertices of G. Magnant, Wang and Yuan conjectured that μ (G)≤max{n/δ +1, ( Δ -δ) n/( Δ +δ) } . In this work, we give a positive answer to this conjecture, for Δ≥ 2 δ.
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