Given a graph and two functions and with for each , a -quasifactor in is a subgraph of such that for each vertex in ; in the particular case when , we say that is a -quasifactor. A subset of vertices of is said -quasifactorable in if there exists some -quasifactor that contains all the vertices of . In this paper, we give several results on the -quasifactorability of a vertex subset which are related to minimum degree, degree sum, independence number and neighborhood union conditions.
This work was done while this author was visiting L.R.I. under an exchange program and partially supported by the National Natural Science Foundation of People's Republic of China.