We study conditions for a simple graph G or its complement Ḡ to have a 1-factor. Let G be a graph of even order n and denote by ir(G) the difference between the maximum degree and the minimum degree of G. We prove that if both G and Ḡ are connected and ir(G) ≤ [1/4n + 1], then either G or Ḡ has a 1-factor with the inequality being sharp.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics