If G is a minimally 3-connected graph and C is a double cover of the set of edges of G by irreducible walks, then |E(G)| ≥ 2| C| - 2.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1218, author = {V\'\i ctor Neumann-Lara and Eduardo Rivera-Campo and Jorge Urrutia}, title = {A note on minimally 3-connected graphs}, journal = {Discussiones Mathematicae Graph Theory}, volume = {24}, year = {2004}, pages = {115-123}, zbl = {1054.05084}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1218} }
Víctor Neumann-Lara; Eduardo Rivera-Campo; Jorge Urrutia. A note on minimally 3-connected graphs. Discussiones Mathematicae Graph Theory, Tome 24 (2004) pp. 115-123. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1218/
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