For connected n-vertex graphs with n>=25 and 0<=alpha<2/3, A_alpha-spectral radius at least that of K1 joined to (K_{n-2} plus an isolated vertex) guarantees a {P3,P4,P5}-factor unless the graph is the boundary graph itself.
Zhou, Some results on path-factor critical avoidable graphs , Discussiones Mathematicae Graph Theory 43(1) (2023) 233–244
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An A{\alpha}-spectral radius for the existence of {P3, P4, P5}-factors in graphs
For connected n-vertex graphs with n>=25 and 0<=alpha<2/3, A_alpha-spectral radius at least that of K1 joined to (K_{n-2} plus an isolated vertex) guarantees a {P3,P4,P5}-factor unless the graph is the boundary graph itself.