Bonds intersecting cycles in a graph (Q2568498)

A bond of a graph \(G\) is a minimum cut set of \(G\). It is proved that for a \(k\)-connected graph \(G\) with circumference \(c\geq 2k, k\geq 2\), there exists a bond which intersects every cycle of length \(c-k+2\) or greater. This result dualizes a result of the author in [Combinatorica 25, No.~4, 451--463 (2005; Zbl 1090.05039)].