skip to content
A Theorem on Matchings in the Plane. 2. Some Planar Considerations. Preview this item
ClosePreview this item
Checking...

A Theorem on Matchings in the Plane. 2. Some Planar Considerations.

Author: Michael D Plummer; VANDERBILT UNIV NASHVILLE TN.
Publisher: Ft. Belvoir Defense Technical Information Center JAN 1985.
Edition/Format:   Book : English
Database:WorldCat
Summary:
Let G be a graph with (V(G)) = p points and (E(G)) = q lines. A matching in G is any set of lines in E(G) no two of which are adjacent. Matching M in G is said to be a perfect matching, or p.m., if every point of G is covered by a line of M. Let G be any graph with a perfect matching and suppose positive integer n <or minus (p - 2)/2. Then G is n extendable if every matching in G containing n lines is a subset of  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Document Type: Book
All Authors / Contributors: Michael D Plummer; VANDERBILT UNIV NASHVILLE TN.
OCLC Number: 227672076
Description: 16 p.

Abstract:

Let G be a graph with (V(G)) = p points and (E(G)) = q lines. A matching in G is any set of lines in E(G) no two of which are adjacent. Matching M in G is said to be a perfect matching, or p.m., if every point of G is covered by a line of M. Let G be any graph with a perfect matching and suppose positive integer n <or minus (p - 2)/2. Then G is n extendable if every matching in G containing n lines is a subset of a p.m. The concept of n-extendability gradually evolved from the study of elementary bipartite graphs (which are 1-extendable) and then of arbitrary 1-extendable (or 'matching-covered') graphs. The study of n-extendability for arbitrary n was begun by the author (1980). This paper is concerned with matchings in planar graphs. When we speak of an imbedding of planar graph G in the plane, we mean a topological imbedding in the usual sense and would remind the reader that such an imbedding is necessarily 2-cell. If we wish to refer to a planar graph G together with an imbedding of G in the plane, we shall speak of the plane graph G. The main result of this paper is to show that no planar graph is 3-extendable.

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.

Similar Items

Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


<http://www.worldcat.org/oclc/227672076>
library:oclcnum"227672076"
library:placeOfPublication
library:placeOfPublication
owl:sameAs<info:oclcnum/227672076>
rdf:typeschema:Book
schema:about
schema:about
schema:about
schema:about
schema:about
schema:contributor
schema:contributor
schema:datePublished"1985"
schema:datePublished"JAN 1985"
schema:description"Let G be a graph with (V(G)) = p points and (E(G)) = q lines. A matching in G is any set of lines in E(G) no two of which are adjacent. Matching M in G is said to be a perfect matching, or p.m., if every point of G is covered by a line of M. Let G be any graph with a perfect matching and suppose positive integer n "@en
schema:exampleOfWork<http://worldcat.org/entity/work/id/137372252>
schema:inLanguage"en"
schema:name"A Theorem on Matchings in the Plane. 2. Some Planar Considerations."@en
schema:numberOfPages"16"
schema:publisher
schema:url

Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.