报告人：周向前，Wright State University, Dayton Ohio USA
报告时间：2017年6月27日14:00-16:00
报告地点：数计学院4号楼229室
报告题目：Minimally k-connected Graphs and Matroids
报告摘要：A matroid M is a pair (E, \mathcal{I}) where E is a finite set, called the ground set of M, and \mathcal{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 \in j-i such that i \cup {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. So we may view matroids as a generalization of graphs.
A graph is minimally k-connected if it is k-connected and the deletion of an arbitrary edge produces a subgraph that is no longer k-connected. Halin showed that every minimally k-connected graph has a degree-k vertex. Analogous results for matroids were only proved for some small values of k. We will give a short survey on these results and show some recent progress on the problem.
