Open math1um opened 7 years ago
def kashin_konyagin_property(g):
upper_bound = 2^(2/3)*g.order()^(1/3)
if (independence_number(g) <= 2):
return upper_bound
else:
return bool(independence_number(g) <= upper_bound)
This returns True/False for graphs with an independence number > 2 or the upper bound for the independence number if it is <= 2. Does this look okay?
They proved: For graphs with alpha<=2, lovasz_theta <= 2^(2/3)*n^(1/3), where n = order.
It is possible some graphs with alpha > 2 also have this property.
from p.47 of Knuth paper: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v1i1a1