Flip graphs of matroids are expanders: https://gilkalai.wordpress.com/2018/12/12/nima-anari-kuikui-liu-shayan-oveis-gharan-and-cynthia-vinzant-solved-the-mihail-vazirani-conjecture/

Gil Kalai reports on a new proof by Nima Anari, Kuikui Liu, Shayan Oveis Gharan, and Cynthia Vinzant of a conjecture by Milena Mihail and Umesh Vazirani that any subset \( S \) of at most half of the bases of a matroid has at least \( |S| \) flips to a base outside \( S \).

Based on a preprint at https://arxiv.org/abs/1811.01816, via https://plus.google.com/117271457236114081433/posts/BBWDnosHkqy