Extensions of Tutte's wheels-and-whirls theorem
Tutte's wheels-and-whirls theorem states that if M is a 3-connected matroid and, for every element e, both the deletion and the contraction of e destroy 3-connectivity, then M is a wheel or a whirl. We prove some extensions of this theorem, one of which states that if M is 3-connected and has both a wheel and a whirl minor, then either M has only seven elements or there is some element the deletion or contraction of which maintains 3-connectivity and leaves a matroid with both a wheel and a whirl minor. © 1992.
Publication Source (Journal or Book title)
Journal of Combinatorial Theory, Series B
Coullard, C., & Oxley, J. (1992). Extensions of Tutte's wheels-and-whirls theorem. Journal of Combinatorial Theory, Series B, 56 (1), 130-140. https://doi.org/10.1016/0095-8956(92)90012-M