On removable cycles through every edge

Mader and Jackson independently proved that every 2‐connected simple graph G with minimum degree at least four has a removable cycle, that is, a cycle C such that G / E ( C ) is 2‐connected. This paper considers the problem of determining when every edge of a 2‐connected graph G , simple or not, can be guaranteed to lie in some removable cycle. The main result establishes that if every deletion of two edges from G remains 2‐connected, then, not only is every edge in a removable cycle but, for every two edges, there are edge‐disjoint removable cycles such that each contains one of the distinguished edges. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 155–164, 2003