Strengthened chain theorems for different versions of 4-connectivity
Abstract
The chain theorem of Tutte states that every 3-connected graph can be constructed from a wheel Wn by repeatedly adding edges and splitting vertices. It is not difficult to prove the following strengthening of this theorem: every non-wheel 3-connected graph can be constructed from W4 by repeatedly adding edges and splitting vertices. In this paper we similarly strengthen several chain theorems for various versions of 4-connectivity.
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