(1,f)-Factors of Graphs with Odd Property

作者:Egawa, Yoshimi; Kano, Mikio*; Yan, Zheng
来源:Graphs and Combinatorics, 2016, 32(1): 103-110.
DOI:10.1007/s00373-015-1558-x

摘要

Let be a graph and be a function. We denote by the number of odd components of . We prove that if for all , then has a -factor such that, for every vertex of , if is even, then , and otherwise . This theorem is a generalization of both the -odd factor theorem and a recent result on -factors by Lu and Wang. We actually prove a result stronger than the above theorem.