Notes on Fractional (1, f)-Odd Factors of Graphs

摘要

Let G be a simple graph and f an odd integer-valued function defined on V(G). A spanning subgraph F of G is called a fractional (1, f)-odd factor if d_F(v) ∈ {1,3, …, f(v)} for all v ∈ V(G), where d_F(v) is the fractional degree of v in F. In this paper, we discuss the existence for a graph to have a fractional (1, f)-odd-factor. A necessary and sufficient condition for a tree to have a fractional (l,f)-odd factor is given.