On quasifactorability in graphs Original Research Article

Given a graph G and two functions f and g:V(G)→Z+ with f(v)⩾g(v) for each v∈V(G), a (g,f)-quasifactor in G is a subgraph Q of G such that for each vertex v in V(Q), g(v)⩽dQ(v)⩽f(v); in the particular case when ∀v∈V(Q), f(v)=g(v)=k∈N, we say that Q is a k-quasifactor. A subset S of vertices of G is said (g,f)-quasifactorable in G if there exists some (g,f)-quasifactor that contains all the vertices of S. In this paper, we give several results on the 2-quasifactorability of a vertex subset which are related to minimum degree, degree sum, independence number and neighborhood union conditions.