Abstract
Let F 7 denote the Fano matroid and e be a fixed element of F 7 . Let P ( F 7 , e ) be the family of matroids obtained by taking the parallel connection of one or more copies of F 7 about e . Let M be a simple binary matroid such that every cocircuit of M has size at least d ⩾3. We show that if M does not have an F 7 -minor, M ≠ F * 7 , and d ⩾( r ( M )+1)/2 then M has a circuit of size r ( M )+1. We also show that if M is connected, e ∈ E ( M ), M does not have both an F 7 -minor and an F * 7 -minor, and M ∉ P ( F 7 , e ), then M has a circuit that contains e and has size at least d +1.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
