Switchings Constrained to 2-Connectivity in Simple Graphs
Richard Taylor · SIAM Journal on Algebraic and Discrete Methods · 1982
This paper follows as a natural extension of the ideas in a previous paper where we showed that any connected graph may be transformed by a sequence of switchings to any other connected graph of the same degree sequence, in such a way that all the intermediate graphs formed are connected. This was done for simple graphs, multigraphs and pseudographs. Here we show that the corresponding result is true for 2-connected simple graphs. The result for multigraphs and pseudographs will appear elsewhere. We also note that for k-connected graphs where $k\geqq 3$, this transformation theorem seems much more difficult to prove and in the last section of this paper we mention these difficulties.