Topic:Reinforcement hypergraph strength
Speaker: Professor Lai Hongjian
Event date: 6/24/2019
Event time: 14:30 pm
Venue: Lecture Hall 1506, Building 9
Sponsor: School of Mathematics and Statistics, Institute of Science and Technology
Abstract: Given a network modeled as a graph $G$ and an integer $k > 0$, what is the smallest effort to convert $G$ into a graph with the same set of vertices and with $k$-edge-disjoint spanning trees? Payanin [European Journal of Combinatorics, 7 (1986) 263-270] proposed two conjectures on using minimum effort to convert a graph into one that has $k$-edge-disjoint spanning trees by edge-switching. One of the conjectures was proved in [European Journal of Combinatorics, 17 (1996) 447-450]. The matroidal version of the problem of adding the minimum number of edges to result in a graph with $k$-edge-disjoint spanning trees is done in Ping Li’s dissertation(see [Applied Mathematics, 1 (2010), 244-249]). We in this talk will report the recent progresses of such reinforcement problems in hypergraphs.