In this paper, we prove that a matroid with at least two elements is connected if and only if it can be obtained from a loop by a nonempty sequence of non-trivial single-element extensions and series extensions.
Citation
M.M. Shikare, B.N. Waphare . A Chracterization of Connected Matroids[J], Ars Combinatoria, Volume 086. 345-347. .
