Journal of Graph Algorithms and Applications
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Flows in One-Crossing-Minor-Free Graphs
Vol. 17, no. 3, pp. 201-220, 2013. Regular paper.
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(nlogn) time. In particular, maximum flows in directed K3,3-minor-free graphs and directed K5-minor-free graphs can be computed in O(nlogn) time without additional assumptions.
Submitted: August 2012.
Reviewed: January 2013.
Revised: February 2013.
Accepted: February 2013.
Final: February 2013.
Published: March 2013.
Communicated by Susanne Albers