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Degree sequence conditions for equal edge-connectivity and minimum degree, depending on the clique number

✍ Scribed by Lutz Volkmann

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
87 KB
Volume
42
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

Using the well‐known Theorem of Turán, we present in this paper degree sequence conditions for the equality of edge‐connectivity and minimum degree, depending on the clique number of a graph. Different examples will show that these conditions are best possible and independent of all the known results in this area. © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 234–245, 2003

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A sufficient condition for equality of edge-connectivity and minimum degree of a graph
✍ Donald L. Goldsmith; Roger C. Entringer 📂 Article 📅 1979 🏛 John Wiley and Sons 🌐 English ⚖ 184 KB 👁 1 views

## Abstract Let __G__ be a connected graph of order __p__ ≥ 2, with edge‐connectivity κ~1~(__G__) and minimum degree δ(__G__). It is shown her ethat in order to obtain the equality κ~1~(__G__) = δ(__G__), it is sufficient that, for each vertex __x__ of minimum degree in __G__, the vertices in the n