Spectral conditions for graphs to contain k-factors

Let G be a graph. The spectral radius $ρ(G)$ of G is the largest eigenvalue of its adjacency matrix. For an integer k≥1, a k-factor of G is a k-regular spanning subgraph of G. Assume that k and n are integers satisfying k≥2,kn≡0~(2) and n≥max²+6k+7,20k+10\. Let G be a graph of order n and with minimum degree at least k. In this paper, we give a sharp lower bound of $ρ(G)$ to guarantee that G contains a k-factor.