### 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 δ_{U} + δ_{V} ≥ n + 2 as long as n is sufficiently large in terms of κ and δ(G) ≥ n/200κ + 1.

Original language | English (US) |
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Pages (from-to) | 486-504 |

Number of pages | 19 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 24 |

Issue number | 2 |

DOIs | |

State | Published - 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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## Cite this

Czygrinow, A., Debiasio, L., & Kierstead, H. (2010). 2-Factors of bipartite graphs with asymmetric minimum degrees.

*SIAM Journal on Discrete Mathematics*,*24*(2), 486-504. https://doi.org/10.1137/080739513