Speaker：Rong Luo, Department of Mathematics West Virginia University Morgantown
Time: 2017-06-07 10:00-11:00
Place：Room 1518，School of Mathematical Sciences
Detail： The concept of group connectivity was introduced by Jaeger, Linial, Payan, and Tarsi (Journal Combinatorial Theory, Ser. B, 1992) as a generalization of nowhere-zero group flows. Let A be an Abelian group. An A-connected graphs are contractible configurations of A-flow and play an important role in the study of group flows because of the fact: if H is A-connected, then any supergraph G of H (i.e. G contains H as a subgraph) admits a nowhere-zero A-flow if and only if G/H does. It is known that an A-connected graph cannot be very sparse. How dense could an A-connected graph be? This motivates us to study the extremal problem: find the maximum integer k, denoted ex(n, A), such that every graph with at most k edges is not A-connected. We determine the exact values for all finite cyclic groups. As a corollary, we present a characterization of all Zk-connected graphic sequences. As noted by Jaeger, Linial, Payan, and Tarsi, there are Z5-connected graph that are not Z6-connected. We also prove that every Z3-connected graph contains two edge-disjoint spanning trees, which implies that every Z3-connected graph is also A-connected for any Abelian group A with order at least 4. In the second part of the talk, I will introduce the concept of group connectivity of signed graphs and present some basic properties of group connectivities of signed graphs.
According to the latest Nature Publishing Index (NPI) Asia-Pacific and The Nature Publishing Index China, University of Science and Technology of China tops in Chinese universities again. The rankings are based on the number of papers that were published in Nature journals during the last 12 months.
This article came from News Center of USTC.