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 K₅ (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.