Complete Closure and Regular Factors

Abstract

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