The Connectivity and Diameter of Second Order Circuit Graphs of Matroids

摘要

Let C _2(M) be the second order circuit graph of a simple connected matroid M, then C _2(M) is 2-connected if M has more than one circuit and M is not a line. Moreover, C _2(M) has diameter at most two if and only if M does not have any restriction isomorphic to U _(2,6).