K3,3 Minors and the Maximum-Flow Problem

Authors

  • Donald Wagner Office of Naval Research, Arlington, VA 22203, USA

Keywords:

maximum-flow problem, planar graphs, graph decomposition

Abstract

Let G be a graph, and let e be an edge of G. The main result of this paper is that any instance of the maximum-flow problem on G having e as the "return" edge can be solved in linear time provided G does not have a K3,3 minor containing e. The primary tool in proving this result is a new graph decomposition. In particular, it is shown that if G is 3-connected and does not have a K3,3 minor containing e, then it can be decomposed into planar graphs, "almost" planar graphs, and copies of K5.

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Published

2008-03-25

How to Cite

Wagner, D. (2008). K3,3 Minors and the Maximum-Flow Problem. Algorithmic Operations Research, 3(1). Retrieved from https://journals.lib.unb.ca/index.php/AOR/article/view/4176

Issue

Vol. 3 No. 1 (2008)

Section

Articles

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