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Fast Backtracking Principles Applied to Find New Cages
 Ninth Annual ACMSIAM Symposium on Discrete Algorithms (SODA
, 1998
"... We describe how standard backtracking rules of thumb were successfully applied to the problem of characterizing (3; g) cages, the minimum order 3regular graphs of girth g. It took just 5 days of cpu time (compared to 259 days for previous authors) to verify the (3; 9)cages, and we were able to c ..."
Abstract

Cited by 9 (3 self)
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We describe how standard backtracking rules of thumb were successfully applied to the problem of characterizing (3; g) cages, the minimum order 3regular graphs of girth g. It took just 5 days of cpu time (compared to 259 days for previous authors) to verify the (3; 9)cages, and we were able to confirm that (3; 11)cages have order 112 for the first time ever. The lower bound for a (3; 13)cage is improved from 196 to 202 using the same approach. Also, we determined that a (3; 14)cage has order at least 258. 1 Cages In this paper, we consider finite undirected graphs. Any undefined notation follows Bondy and Murty [7]. The girth of a graph is the size of a smallest cycle. A (r; g) cage is an rregular graph of minimum order with girth g. It is known that (r; g)cages always exist [11]. Some nice pictures of small cages are given in [9, pp. 5458]. The classification of the cages has attracted much interest amongst the graph theory community, and many of these have special nam...