Flows in One-Crossing-Minor-Free Graphs
arXiv:1007.1484 · doi:10.7155/jgaa.00291
Abstract
We study the maximum flow problem in directed H-minor-free graphs where H can be drawn in the plane with one crossing. If a structural decomposition of the graph as a clique-sum of planar graphs and graphs of constant complexity is given, we show that a maximum flow can be computed in O(n log n) time. In particular, maximum flows in directed K_{3,3}-minor-free graphs and directed K_5-minor-free graphs can be computed in O(n log n) time without additional assumptions.
16 pages, 4 figures