Note on parity factors of regular graphs

TL;DR

This paper establishes a sufficient and sharp condition based on edge-connectivity for the existence of parity factors in regular graphs, advancing understanding of graph factorization.

Contribution

It provides a new sufficient condition for parity factors in regular graphs, which is proven to be sharp, enhancing theoretical graph factorization criteria.

Findings

Established a sufficient condition for parity factors in regular graphs

Proved the condition is sharp

Contributed to graph factorization theory

Abstract

In this paper, we obtain a sufficient condition for the existence of parity factors in a regular graph in terms of edge-connectivity. Moreover, we also show that our condition is sharp.