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On Canonical Concurrent Flows, Crossing Number and Graph Expansion

Published online by Cambridge University Press:  12 September 2008

Farhad Shahrokhi  and
László A. Székely
Farhad Shahrokhi
Affiliation:
University of North Texas, Denton TX
László A. Székely
Affiliation:
Eötvös University, Budapest and University of New Mexico, Albuquerque NM
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Abstract

We define and efficiently compute the canonical flow on a graph, which is a certain feasible solution for the concurrent flow problem and exhibits invariance under the action of the automorphism group of the graph. Using estimates for the congestion of our canonical flow, we derive lower bounds on the crossing number, bisection width, and the edge and vertex expansion of a graph in terms of sizes of the edge and vertex orbits and the average distance in the graph. We further exhibit classes of graphs for which our lower bounds are tight within a multiplicative constant. Also, in cartesian product graphs a concurrent flow is constructed in terms of the concurrent flows in the factors, and in this way lower bounds for the edge and vertex expansion of the power graphs are derived in terms of that of the original graph.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 4 , December 1994 , pp. 523 - 543
Copyright
Copyright © Cambridge University Press 1994

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