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A  graph G gives rise to a matroid M(G) where the ground set is E(G) and a subset  of E(G) is independent if it spans a forest. So we may view matroids as a  generalization of graphs.

A  graph is minimally k-connected if it is k-connected and the deletion of an  arbitrary edge produces a subgraph that is no longer k-connected. Halin showed  that every minimally k-connected graph has a degree-k vertex. Analogous results  for matroids were only proved for some small values of k. We will give a short  survey on these results and show some recent progress on the  problem.