2-Factors of bipartite graphs with asymmetric minimum degrees

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Abstract

Let G and H be balanced U, V-bigraphs on 2n vertices with δ (H) ≤ 2. Let κ be the number of components of H, δU := min{deg G(υ): υ ∈ U} and δv := min{deg G(υ): υ G V}. We prove that if n is sufficiently large and δU +δV ≥ n+κ, then G contains H. This answers a question of Amar in the case that n is large. We also show that G contains H even when δU + δV ≥ n + 2 as long as n is sufficiently large in terms of κ and δ(G) ≥ n/200κ + 1.

Original languageEnglish (US)
Pages (from-to)486-504
Number of pages19
JournalSIAM Journal on Discrete Mathematics
Volume24
Issue number2
DOIs
StatePublished - Jul 16 2010

Keywords

  • 2-factors
  • Bipartite graphs
  • Blow-up lemma
  • Regularity lemma
  • Spanning cycles

ASJC Scopus subject areas

  • Mathematics(all)

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