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Computational determination of (3, 11) and (4, 7) cages

Exoo, Geoffrey; McKay, Brendan; Myrvold, Wendy; Nadon, Jacqueline


A (k,g)-graph is a k-regular graph of girth g, and a (k,g)-cage is a (k,g)-graph of minimum order. We show that a (3,11)-graph of order 112 found by Balaban in 1973 is minimal and unique. We also show that the order of a (4,7)-cage is 67 and find one example. Finally, we improve the lower bounds on the orders of (3,13)-cages and (3,14)-cages to 202 and 260, respectively. The methods used were a combination of heuristic hill-climbing and an innovative backtrack search.

CollectionsANU Research Publications
Date published: 2011
Type: Journal article
Source: Journal of Discrete Algorithms (Amsterdam)
DOI: 10.1016/j.jda.2010.11.001


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