Speaker:Jørgen Bang-Jensen, University of Southern Denmark

Inviter: Yan Jin, Professor, School of Mathematics, Shandong University

Date: Mar.17,18, 2021

Time: Mar. 17 8:00 p.m. Mar. 18 3:30 p.m.

Location: Zoom ID: 546 268 6882 Password：526874

Abstract:

Bipolar orientation of G is an acyclic orientation D of G which has a unique source and a unique sink. Our interest is to study graphs which admit a bipolar orientation that contains a pair of arc-disjoint out-branching and in-branching (such an orientation is called good). Thomassen proved that deciding whether a digraph contains a pair of arc-disjoint out-branching and in-branching is an NP-complete problem. A 2T-graph is a graph whose edge set can be decomposed into two edge-disjoint spanning trees. We show connections between the problem of deciding whether a given 2T-graph has a good orientation and matroid theory. We also illustrate to deciding the existence of a good orientation of a 2T-graph can be quite complicated and it is an open problem whether there is a polynomial algorithm for the problem. We also show a number of results on a special class of 2T-graphs, called quartics in which every vertex has degree 3 or 4. Even for this class it is open whether there is a polynomial algorithm. This is joint work with Bessy, Huang, Jackson and Kriesell.

Bio:

Jørgen Bang-Jensen, University of Southern Denmark

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/146660.htm