analyze-cycle.py

from graph_tools.base import *
from graph_tools.parameters import *
from sage.all import *
from collections import namedtuple
from itertools import *


def calc(s):
  b = list(CircuitDoubleCover.enumerate_boundaries(s))
  m = dict()

  _bmap = { x: i for i, x in enumerate(b) }
  def eval_(g):
    ret = set()
    g_ = FakeGadget(g.size(), g.eval(CircuitDoubleCover))
    for c, cb in enumerate(b):
      cg = FakeGadget(g.size(), [ Boundary(cb, 1) ])
      v = Gadget.join(
        [ cg, g_ ],
        [ ((1, i), (2, i)) for i in range(1, s+1) ],
        []
      ).eval(CircuitDoubleCover)
      if v > 0: ret.add(c)

    return ret

  ret = namedtuple("calc_ret", ["boundaries", "eval", "map"])
  ret.boundaries = b
  ret.eval = eval_
  ret.map = lambda x: _bmap[x]

  return ret


def C_k(k):  
  return Gadget.join(
    [CUBIC_VERTEX]*k,
    [ ((i+1, 2), (((i+1) % k) + 1, 1)) for i in range(k) ],
    [ (i+1, 3) for i in range(k) ]
  )

def G_k(k):
  return Gadget.join(
    [CUBIC_VERTEX]*k,
    [ ((i+1, 2), (((i+1) % (k-1)) + 1, 1)) for i in range(k-1) ] + [ ((1,3), (k,1)) ],
    [ (i+2, 3) for i in range(k-2) ] + [ (k, 2), (k, 3) ]
  )

k = 6
c = calc(k)
e = c.eval(C_k(k))
f = c.eval(G_k(k))

print(len(e))
print(len(f))
print(len(set(f).intersection(set(e))))