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Dynamic cage survey. (English) Zbl 1169.05336

Summary: A \((k, g)\)-cage is a \(k\)-regular graph of girth g of minimum order. In this survey, we present the results of over 50 years of searches for cages. We present the important theorems, list all the known cages, compile tables of current record holders, and describe in some detail most of the relevant constructions.
Version 2 published: May 8, 2011 (54 pages)
Version 3 published: July 26, 2013 (55 pages)

MSC:

05C35 Extremal problems in graph theory
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05-02 Research exposition (monographs, survey articles) pertaining to combinatorics

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