Inductive tools for handling internally 4-connected binary matroids
Document Type
Lecture
Publication Date
2-13-2014
Abstract
A binary matroid is internally 4-connected if it does not break up as a 1-, 2-, or 3-sum. The class of such matroids includes the cycle matroids of internally 4-connected graphs, those 3-connected simple graphs that are 4-connected except for the possible presence of degree-3 vertices. Given internally 4-connected binary matroids M and N where N is a proper minor of M, we are interested in removing a small number of elements from M to obtain another internally 4-connected matroid that maintains an N-minor. As Johnson and Thomas noted in 2002, even for graphic matroids, we cannot always succeed in doing this. We are, however, able to show that we can obtain the desired theorem if we replace the notion of “removing a small number of elements” with “performing a small number of simple moves.” This talk will formalize these notions and give an update on our work toward this end.
Relational Format
presentation
Recommended Citation
Chun, Carolyn, "Inductive tools for handling internally 4-connected binary matroids" (2014). Colloquium. 26.
https://egrove.olemiss.edu/math_colloquium/26
