报告人：Rong Luo 

Department of MathematicsWest Virginia UniversityMorgantown

报告时间：6月7号 10:00-11:00

地点：1518

摘要： The concept of group connectivity was introduced by Jaeger, Linial, Payan,and Tarsi (Journal Combinatorial Theory, Ser. B, 1992) as a generalization ofnowhere-zero group flows. Let A be an Abelian group. An A-connected graphsare contractible configurations of A-flow and play an important role in the studyof group flows because of the fact: if H is A-connected, then any supergraphG of H (i.e. G contains H as a subgraph) admits a nowhere-zero A-flow ifand only if G/H does. It is known that an A-connected graph cannot be verysparse. How dense could an A-connected graph be? This motivates us to studythe extremal problem: find the maximum integer k, denoted ex(n, A), such thatevery graph with at most k edges is not A-connected. We determine the exactvalues for all finite cyclic groups. As a corollary, we present a characterizationof all Zk-connected graphic sequences. As noted by Jaeger, Linial, Payan, andTarsi, there are Z5-connected graph that are not Z6-connected. We also provethat every Z3-connected graph contains two edge-disjoint spanning trees, whichimplies that every Z3-connected graph is also A-connected for any Abeliangroup A with order at least 4.In the second part of the talk, I will introduce the concept of group connectivityof signed graphs and present some basic properties of group connectivitiesof signed graphs