On the path partition of graphs

12/24/2022

∙

by   M. Kouider, et al.

∙

0

∙

share

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.