Document Type
Lecture
Publication Date
9-10-2014
Abstract
Kuratowski’s Theorem states that a graph is planar if any only if it has no minor that is isomorphic to K3,3 or K5. Mayhew, Royle and Whittle characterize internally 4-connected binary matroids with no M(K3,3)-minor. Oxley characterizes 3-connected binary matroids without any P9- or P∗9-minor. In this paper, we give a complete characterization of 3-connected binary matroids with no P9-minor. Such a matroid is either one of the non-regular minors of a special 16-element matroid Y16; a 3-connected regular matroid; a binary spike with rank at least four; or is a matroid in an infinite class of matroids called starfishes. This is joint work with Guoli Ding at LSU.
Relational Format
presentation
Recommended Citation
Wu, Haidong, "Characterizing 3-connected binary matroids with no P9-minor" (2014). Combinatorics Seminar. 51.
https://egrove.olemiss.edu/math_combinatorics/51
