Computational determination of (3, 11) and (4, 7) cages
Date
2011
Authors
Exoo, Geoffrey
McKay, Brendan
Myrvold, Wendy
Nadon, Jacqueline
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Volume Title
Publisher
Elsevier
Abstract
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.
Description
Keywords
Keywords: Backtrack search; Cage; Girth; Hill climbing; Lower bounds; Minimum order; Regular graph; Regular graphs; Graph theory; Heuristic methods Cage; Girth; Regular graph
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Source
Journal of Discrete Algorithms (Amsterdam)
Type
Journal article
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Restricted until
2037-12-31