一、题目

Good acyclic orientations of unions of spanning trees

二、主讲人

Jørgen Bang-Jensen

三、摘要

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

四、主讲人简介

Jørgen Bang-Jensen, University of Southern Denmark

五、邀请人

颜谨 数学学院教授

六、时间

3月17日（周三）20:00

3月18日（周四）15:30

七、地点

Zoom，ID：546 268 6882

Password：526874

八、主办方

山东大学数学学院