Graph minors and graph linkage
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 K5 (the
complete graph with five vertices) or K3,3 (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
Kk 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.