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吴文俊数学重点实验室组合图论系列讲座之一百零三【Xiangqian Zhou】
题目:Induction for 4-connected Matroids and Graphs

报告人:Xiangqian Zhou (Joe)

Wright State University, Dayton Ohio USA and Huaqiao University, Quanzhou Fujian China

时间:6月14日  4:30-5:30

地点:1518

摘要:A matroid M is a pair (E, I) where E is a finite set, called the ground set of M, and I is a non-empty 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 well-known inductive tools for proving results for 3-connected graphs and matroids. In this talk, we will give a survey on induction theorems for various versions of matroid 4-connectivity.

中国科学院吴文俊数学重点实验室