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On Vertices of Degree n in Minimally n-Edge-Connected Graphs

Published online by Cambridge University Press:  12 September 2008

W. Mader
W. Mader
Affiliation:
Institut fur Mathematik, Universität Hannover, Welfengarten 1, D-30167 Hannover
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Abstract

Let G be a minimally n-edge-connected finite simple graph with vertex number |G| ≥ 2n + 2 + [3/n] and let n ≥ 3 be odd. It is proved that the number of vertices of degree n in G is at least ((n − 1 − ∈n)/(2n + 1))|G| + 2 + 2∈n, where ∈n = (3n + 3)/(2n2 − 3n − 3), and that for every n ≡ 3 (mod 4) this lower bound is attained by infinitely many minimally n-edge-connected finite simple graphs.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 4 , Issue 1 , March 1995 , pp. 81 - 95
Copyright
Copyright © Cambridge University Press 1995

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