Computational determination of (3, 11) and (4, 7) cages
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.
|Collections||ANU Research Publications|
|Source:||Journal of Discrete Algorithms (Amsterdam)|
|01_Exoo_Computational_determination_of_2011.pdf||117.59 kB||Adobe PDF||Request a copy|
|02_Exoo_Computational_determination_of_2011.pdf||219.77 kB||Adobe PDF||Request a copy|
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