Complete Closure and Regular Factors

The complete stability \(cs(P_k)\), where \(P_k\) denotes the property of having a \(k\)-factor, satisfies \(cs(P_k) = n + k – 2, \text{ if } 1 \leq k \leq 3\), and \(n + k – 2 \leq cs(P_k) \leq n + k – 1, \text{ if } k \geq 4\). A similar result for bipartite graphs with complete biclosure is proved also.