Peripheral circuits in infinite binary matroids

摘要

A peripheral circuit in a (possibly infinite) matroid M is a circuit C of M such that M/C is connected. In the case of a 3-connected graph G, this is equivalent to C being chordless and G - V(C) being connected. Two classical theorems of Tutte assert that, for a 3-connected graph G: (i) every edge e of G is in two peripheral cycles that intersect just on e and its incident vertices; and (ii) the peripheral cycles generate the cycle space of G [12].