### Abstract

One way to represent a matching in a graph of a set A with a set B is with a one-to-one function m : A → B for which each pair {a, m(a)} is an edge of the graph. If the underlying set of vertices of the graph is linearly ordered and every element of A is less than every element of B, then such a matching is a down-up matching. In this paper we investigate graphs on well-ordered sets of type α and in many circumtances find either large independent sets of type β or down-up matchings with the initial set of some prescribed size γ. In this case we write α → (β, γ-matching).

Original language | English |
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Pages (from-to) | 169-182 |

Number of pages | 14 |

Journal | Discrete Mathematics |

Volume | 95 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Dec 3 1991 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*95*(1-3), 169-182. https://doi.org/10.1016/0012-365X(91)90335-Y

**Matchings from a set below to a set above.** / Erdős, P.; Larson, Jean A.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 95, no. 1-3, pp. 169-182. https://doi.org/10.1016/0012-365X(91)90335-Y

}

TY - JOUR

T1 - Matchings from a set below to a set above

AU - Erdős, P.

AU - Larson, Jean A.

PY - 1991/12/3

Y1 - 1991/12/3

N2 - One way to represent a matching in a graph of a set A with a set B is with a one-to-one function m : A → B for which each pair {a, m(a)} is an edge of the graph. If the underlying set of vertices of the graph is linearly ordered and every element of A is less than every element of B, then such a matching is a down-up matching. In this paper we investigate graphs on well-ordered sets of type α and in many circumtances find either large independent sets of type β or down-up matchings with the initial set of some prescribed size γ. In this case we write α → (β, γ-matching).

AB - One way to represent a matching in a graph of a set A with a set B is with a one-to-one function m : A → B for which each pair {a, m(a)} is an edge of the graph. If the underlying set of vertices of the graph is linearly ordered and every element of A is less than every element of B, then such a matching is a down-up matching. In this paper we investigate graphs on well-ordered sets of type α and in many circumtances find either large independent sets of type β or down-up matchings with the initial set of some prescribed size γ. In this case we write α → (β, γ-matching).

UR - http://www.scopus.com/inward/record.url?scp=0347616617&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347616617&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(91)90335-Y

DO - 10.1016/0012-365X(91)90335-Y

M3 - Article

VL - 95

SP - 169

EP - 182

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -