# Matchings from a set below to a set above

P. Erdős, Jean A. Larson

Research output: Contribution to journalArticle

1 Citation (Scopus)

### 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 169-182 14 Discrete Mathematics 95 1-3 https://doi.org/10.1016/0012-365X(91)90335-Y Published - Dec 3 1991

### Fingerprint

Graph in graph theory
M-function
Ordered Set
Independent Set
Large Set
Linearly

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Theoretical Computer Science

### Cite this

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

In: Discrete Mathematics, Vol. 95, No. 1-3, 03.12.1991, p. 169-182.

Research output: Contribution to journalArticle

Erdős, P. ; Larson, Jean A. / Matchings from a set below to a set above. In: Discrete Mathematics. 1991 ; Vol. 95, No. 1-3. pp. 169-182.
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