2025/09/27 by Abrishami, Tara, Bowler, Nathan, Joó, Attila +2 · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2509.23394
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.