A factor of a graph is a spanning subgraph. Spectral sufficient conditions are provided via spectral radius and signless Laplacian spectral radius for graphs with (i) a matching of given size (particularly, 1-factor) containing any given edge, and (ii) a star factor with a component isomorphic to stars of order two or three containing any given edge, respectively.
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Cai et al. (2024) studied this question.
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