TY - JOUR
T1 - Computational determination of (3,11) and (4,7) cages
AU - Exoo, Geoffrey
AU - McKay, Brendan D.
AU - Myrvold, Wendy
AU - Nadon, Jacqueline
PY - 2011/6
Y1 - 2011/6
N2 - 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.
AB - 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.
KW - Cage
KW - Girth
KW - Regular graph
UR - http://www.scopus.com/inward/record.url?scp=79952362620&partnerID=8YFLogxK
U2 - 10.1016/j.jda.2010.11.001
DO - 10.1016/j.jda.2010.11.001
M3 - Article
SN - 1570-8667
VL - 9
SP - 166
EP - 169
JO - Journal of Discrete Algorithms
JF - Journal of Discrete Algorithms
IS - 2
ER -