Induction for 4connected Matroids and Graphs

[20170614]
Speaker：Xiangqian Zhou (Joe)
Time： 2017614 16:3017:30
Place： Room 1518，School of Mathematical Sciences
Detail：
Wright State University, Dayton Ohio USA and Huaqiao University, Quanzhou Fujian China A matroid M is a pair (E, I) where E is a finite set, called the ground set of M, and I is a nonempty collection of subsets of E, called independent sets of M, such that (1) a subset of an independent set is independent; and (2) if I and J are independent sets with I < J, then exists x ∈ J\I such that I ∪ {x} is independent. A graph G gives rise to a matroid M(G) where the ground set is E(G) and a subset of E(G) is independent if it spans a forest. Another example is a matroid that comes from a matrix over a field F: the ground set E is the set of all columns and a subset of E is independent if it is linearly independent over F. Tutte’s Wheel and Whirl Theorem and Seymour’s Splitter Theorem are two wellknown inductive tools for proving results for 3connected graphs and matroids. In this talk, we will give a survey on induction theorems for various versions of matroid 4connectivity.
Organizer: School of Mathematical Sciences
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