Inductive tools for handling internally 4-connected binary matroids
|Affiliation:||Louisiana State University|
|Room:||Mathematics and Computer Building (MC) 5158|
A matroid is 3-connected if it does not break up as a 1-sum or a 2-sum. Numerous problems for matroids reduce easily to the study of 3-connected matroids. Two powerful inductive tools for dealing with 3-connected matroids are Tutte's Wheels-and-Whirls Theorem and Seymour's Splitter Theorem. For several years, Carolyn Chun, Dillon Mayhew, and I have been seeking analogues of these theorems for internally 4-connected binary ma- troids, that is, binary matroids that do 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. This talk will report on our progress towards ending these analogues.
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