A constructive characterisation of circuits in the simple (2,1)‐sparse matroid
Thomas A. McCourt, Anthony Nixon · Journal of Graph Theory · 2018
Abstract A simple graph is a (2, 1)‐circuit if and for every proper subgraphHofG. Motivated, in part, by ongoing work to understand unique realisations of graphs on surfaces, we derive a constructive characterisation of (2, 1)‐circuits. The characterisation uses the well‐known 1‐extension andX‐replacement operations as well as several summation moves to glue together (2, 1)‐circuits over small cutsets.