A degree condition for the existence of 1-factors in graphs or their complements

Kiyoshi Ando, Atsushi Kaneko, Tsuyoshi Nishimura

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Abstract

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.

Original languageEnglish
Pages (from-to)1-8
Number of pages8
JournalDiscrete Mathematics
Volume203
Issue number1-3
Publication statusPublished - 1999 May 28

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ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

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