co342a7

#!/usr/bin/python
# dx7hymcxnpq
# 2012.06.29

import copy

def chkTups( s, edgeSet ):
    total_incidence = 0
    for edge in edgeSet:
        if s in edge:
            total_incidence += 1
    return ((total_incidence) % 2 == 0)

K5 = [ [1,2], [1,3], [1,4], [1,5], [2,3], [2,4], [2,5], [3,4], [3,5], [4,5] ]
K34 = [ [1,4], [1,5], [1,6], [1,7], [2,4], [2,5], [2,6], [2,7], [3,4], [3,5], [3,6], [3,7] ]
CUBE = [ [1,2], [1,4], [2,3], [3,4], [5,6], [5,8], [6,7], [7,8], [1,5], [2,6], [3,7], [4,8] ]
def powerset( s ):
    if len(s) == 0: return [[]]
    L = powerset( s[1:] )
    M = []
    for k in L:
        p = copy.deepcopy(k)
        if not (s[0] in p): p.append(s[0])
        M.append(k)
        M.append(p)
    return M

Possibilities = powerset(K5)
CycleSpace = []
for subset in Possibilities:
    failed = 0
    # now check all the vertices --
    for i in range(1,6):
        if not chkTups(i,subset): failed = 1
    if not failed:
        CycleSpace.append(subset)

#print "The cycle space is: \n"
#print CycleSpace
print "IT HAS SIZE %s" % len(CycleSpace)

Possibilities = powerset(K34)
CycleSpace = []
for subset in Possibilities:
    failed = 0
    for i in range(1,8):
        if not chkTups(i, subset): failed = 1
    if not failed:
        CycleSpace.append(subset)

print "IT HAS SIZE %s" % len(CycleSpace)

Possibilities = powerset(CUBE)
CycleSpace = []
for subset in Possibilities:
    failed = 0
    for i in range(1,9):
        if not chkTups(i, subset): failed = 1
    if not failed:
        CycleSpace.append(subset)

print "IT HAS SIZE %s" % len(CycleSpace)