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Weakly 3-Connected Graphs

Published online by Cambridge University Press:  07 June 2006

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

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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.

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Type
Paper
Copyright
2006 Cambridge University Press