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Pegging Graphs Yields a Small Diameter

Published online by Cambridge University Press:  24 August 2010

STEFANIE GERKE
Affiliation:
Mathematics Department, Royal Holloway College, University of London, Egham, TW20 0EX, UK (e-mail: stefanie.gerke@rhul.ac.uk)
ANGELIKA STEGER
Affiliation:
Institute for Theoretical Computer Science, ETH Zurich, CH-8092 Zurich, Switzerland (e-mail: steger@inf.ethz.ch)
NICHOLAS WORMALD
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo ON, N2L 3G1, Canada (e-mail: nwormald@uwaterloo.ca)

Abstract

We consider the following process for generating large random cubic graphs. Starting with a given graph, repeatedly add edges that join the midpoints of two randomly chosen edges. We show that the growing graph asymptotically almost surely has logarithmic diameter. This process is motivated by a particular type of peer-to-peer network. Our method extends to similar processes that generate regular graphs of higher degree.

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Paper
Copyright
Copyright © Cambridge University Press 2010

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References

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