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Weakly 3-Connected Graphs

Published online by Cambridge University Press:  07 June 2006

DONALD K. WAGNER
DONALD K. WAGNER
Affiliation:
Mathematical, Computer, and Information Sciences Division, Office of Naval Research, Arlington, VA 22203, USA (e-mail: wagnerd@onr.navy.mil)
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Abstract

A 3-connected graph $G$ is weakly 3-connected if, for every edge $e$ of $G$, at most one of $G\backslash e$ and $G/e$ is 3-connected. The main result of this paper is that any weakly 3-connected graph can be reduced to $K_4$ by a sequence of simple operations. This extends a result of Dawes [5] on minimally 3-connected graphs.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 15 , Issue 4 , July 2006 , pp. 605 - 617
Copyright
2006 Cambridge University Press

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