Relations between the Circumference and <Emphasis Type="Italic">e</Emphasis>-Circumference of a Matroid

For a connected matroid with at least two elements, let c be the maximum size of a circuit and let c _e be the maximum size of a circuit that contains an element e. In 2001, Wu prove that . In this note, we characterize the matroids that attain this bound. This characterization is used to generalize another result of Wu. Manol Lemos: The author is partially supported by CNPq (Grants No. 476224/04-7 and 301178/05-4) and FAPESP/CNPq (Grant No. 2003/09925-5). Received: October 13, 2006. Final version received: November 6, 2007.