Gexin Yu

*
Graph minors and graph linkage
*

**Abstract:**
Graph minors are very important structures in graphs. Many central results
and problems in graph theory are stated in terms of graph minors. For example,
a graph is planar if and only if it doesn't contains K_{5} (the
complete graph with five vertices) or K_{3,3 } (the complete bipartite
graph with three vertices on each side) as minors. Another example,
Hadwiger's Conjecture, states that a k-chromatic graph contains a copy of
K_{k} as a minor.
We will talk about graph linkage, a key tool in the study of graph minors. We will also study the connectivity of minimal counterexamples to Hadwiger's Conjecture, with the help of graph linkage.