The connectivity of the basis graph of a branching greedoid
Hajo J. Broersma, Xueliang Li · Journal of Graph Theory · 1992
Abstract A result of Korte and Lovász states that the basis graph of every 2‐ connected greedoid is connected. We prove that the basis graph of every 3‐connected branching greedoid is (δ ‐‐ 1)‐connected, where δ is the minimum in‐degree (disregarding the root) of the underlying rooted directed (multi) graph. We also give examples showing that this results is (in some sense) best possible.