On removable circuits in graphs and matroids
Mader proved that every 2-connected simple graph G with minimum degree d exceeding three has a cycle C, the deletion of whose edges leaves a 2-connected graph. Jackson extended this by showing that C may be chosen to avoid any nominated edge of G and to have length at least d-1. This article proves an extension of Jackson's theorem. In addition, a conjecture of Goddyn, van den Heuvel, and McGuinness is disproved when it is shown that a natural matroid dual of Mader's theorem fails. © 1999 John Wiley & Sons, Inc.
Publication Source (Journal or Book title)
Journal of Graph Theory
Lemos, M., & Oxley, J. (1999). On removable circuits in graphs and matroids. Journal of Graph Theory, 30 (1), 51-66. https://doi.org/10.1002/(SICI)1097-0118(199901)30:1<51::AID-JGT6>3.0.CO;2-7