Sufficient conditions for component factors in a graph

Let G be a graph and ℋ be a set of connected graphs. A spanning subgraph H of G is called an ℋ –factor if each component of H is isomorphic to a member of ℋ . In this paper, we first present a lower bound on the size (resp. the spectral radius) of G to guarantee that G has a {P_2, C_n: n≥ 3} –factor (or a perfect k–matching for even k) and construct extremal graphs to show all this bounds are best possible. We then provide a lower bound on the signless laplacian spectral radius of G to ensure that G has a {K_1,j:1≤ j≤ k} –factor, where k≥ 2 is an integer. Moreover, we also provide some Laplacian eigenvalue (resp. toughness) conditions for the existence of {P_2, C_n:n≥ 3} –factor, P_≥ 3 –factor and {K_1,j: 1≤ j≤ k} –factor in G, respectively. Some of our results extend or improve the related existing results.