The Spectral Radius and P≥ℓ-Factors of Graphs Involving Minimum Degree.

For an integer ℓ ≥ 2 , a P ≥ ℓ -factor of a graph G is a spanning subgraph in which each component is a path of order at least ℓ . In this paper, we characterize the extremal graphs with maximum spectral radius among all connected graphs of given order with prescribed minimum degree and without a P ≥ 2 -factor or a P ≥ 3 -factor. This generalizes the result in Li and Miao (Discrete Math 344:112588, 2021). [ABSTRACT FROM AUTHOR]