Pegging graphs yields a small diameter

Authors:
Stefanie Gerke;Angelika Steger;Nicholas Wormald
Affiliations:
Mathematics department, royal holloway college, university of london, egham, tw20 0ex, uk (e-mail: stefanie.gerke@rhul.ac.uk);Institute for theoretical computer science, eth zurich, ch-8092 zurich, switzerland (e-mail: steger@inf.ethz.ch);Department of combinatorics and optimization, university of waterloo, waterloo on, n2l 3g1, canada (e-mail: nwormald@uwaterloo.ca)
Venue:
Combinatorics, Probability and Computing
Year:
2011

Citing 4
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Sampling regular graphs and a peer-to-peer network

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Short cycle distribution in random regular graphs recursively generated by pegging

Random Structures & Algorithms - Proceedings of the Thirteenth International Conference “Random Structures and Algorithms” held May 28–June 1, 2007, Tel Aviv, Israel
Connectivity of random regular graphs generated by the pegging algorithm

Journal of Graph Theory

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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.