Matchings from a set below to a set above

P. Erdős, Jean A. Larson

Research output: Article

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 languageEnglish
Pages (from-to)169-182
Number of pages14
JournalDiscrete Mathematics
Volume95
Issue number1-3
DOIs
Publication statusPublished - 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: Article

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.
@article{471eba9337d84c76925d82c10ec0b0d9,
title = "Matchings from a set below to a set above",
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).",
author = "P. Erdős and Larson, {Jean A.}",
year = "1991",
month = "12",
day = "3",
doi = "10.1016/0012-365X(91)90335-Y",
language = "English",
volume = "95",
pages = "169--182",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "1-3",

}

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

AN - SCOPUS:0347616617

VL - 95

SP - 169

EP - 182

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -