A generalization of a graph result of D.W. Hall

✍ Scribed by S.R. Kingan

• Book ID: 104113681
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 335 KB
• Volume: 173
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/s0012-365x(96)00100-8

✦ Synopsis

D.W. Hall proved that every simple 3-connected graph with a Ks-minor must have a K3.3-minor, the only exception being Ks itself. In this paper, we prove that every 3-connected binary matroid with an M(Ks)-minor must have an M(K3.3)-or M*(K3,3)-minor, the only exceptions being M(K5), a highly symmetric 12-element matroid which we call T12, and any single-element contraction of T~2.