Fat-triangle linkage and kite-linked graphs


Topic:Fat-triangle linkage and kite-linked graphs

Speaker: Professor Yu Gexin

Event date: 7/27/2019

Event time: 15:00 pm

Venue: Lecture Hall 204,Building 9

Sponsor: School of Mathematics and Statistics, Institute of Science and Technology

Abstract: For amultigraph H, a graph G is H-linked if every injective mapping φ:V(H)→V(G) can be extended toan H-subdivision in G. We study the minimum connectivity required for a graphto be H-linked. A k-fat-triangle Fk is a multigraph with three vertices and a totalof k edges. We determine a sharp connectivity requirement for a graph to be Fk-linked. In particular, any k-connected graph is Fk-linked when Fk isconnected. A kite is the graph obtained from K4 by removing two edges at avertex. As a nontrivial application of Fk-linkage, we then prove that every 8-connected graph is kite-linked, which shows that the required connectivity for a graph to be kite-linked is 7 or 8.