On elements in small cocircuits in minimally k-connected graphs and matroids

We give a lower bound on the number of edges meeting some vertex of degree k in terms of the total number of edges in a minimally k-connected graph. This lower bound is tight if k is two or three. The extremal graphs in the case that k=2 are characterized. We also give a lower bound on the number of...

Full description

Saved in:
Bibliographic Details
Published inDiscrete mathematics Vol. 243; no. 1; pp. 273 - 282
Main Authors Reid, Talmage James, Wu, Haidong
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 2002
Elsevier
Subjects
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Sciences and techniques of general use
Connected graph
Graph theory
Matroid
Graph circuit
Contraction
Online AccessGet full text

Cover

More Information
Summary:We give a lower bound on the number of edges meeting some vertex of degree k in terms of the total number of edges in a minimally k-connected graph. This lower bound is tight if k is two or three. The extremal graphs in the case that k=2 are characterized. We also give a lower bound on the number of elements meeting some 2-element cocircuit in terms of the total number of elements in a minimally 2-connected matroid. This lower bound is tight and the extremal matroids are characterized.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(01)00220-5