Paper
A structure theorem for rooted connectivity in bidirected graphs
Authors
Tara Abrishami, Nathan Bowler, Attila Joó, Florian Reich, Qiuzhenyu Tao
Abstract
Recently, bidirected graphs have received increasing attention from the graph theory community with both structural and algorithmic results. Bidirected graphs are a generalization of directed graphs, consisting of an undirected graph together with a map assigning each endpoint of every edge either sign or . The connectivity properties of bidirected graphs are more complex than those of directed graphs and not yet well understood. In this paper, we show a structure theorem about rooted connectivity in bidirected graphs in terms of directed graphs. As applications, we prove Lovász' flame theorem, Pym's theorem and a strong variant of Menger's theorem for a class of bidirected graphs and provide counterexamples in the general case.