Remarks on orthogonal factorizations of digraphs

Abstract

Let D be a digraph with vertex set V(D) and arc set A(D) and let f=(f⁻, f⁺) be a pair of functions defined on V(D). Let H be a km-subdigraph of D. In this paper, it is proved that every (0, mf−m+1)-digraph has a (0, f)-factorization k-orthogonal to H if f(x)≥3k−2 for each x∈V(D).

Keywords:

• digraph
• subdigraph
• (g, f)-factor
• k-orthogonal factorization

2010 AMS Subject Classifications:

• 05C70
• 05C20

Acknowledgement

The author thank Guizhen Liu, Wei Gao, the anonymous referees and the editor for their helpful comments and valuable suggestions in improving the quality of this paper. Supported by the National Natural Science Foundation of China (Grant No. 11371009).