Reconstruction tester

Independently checkable McKay-style deck comparison.

Tools

bin/geng, bin/labelg, bin/shortg — nauty 2.9.1 (/tmp/nauty2_9_1)
bin/deckrecon — SHA-256 of the nauty-canonical full deck and reduced deck
bin/add_twofactor — overlay every complement 2-factor of given support size
verify_labelg.py — rebuilds cards in Python, canonicalises with labelg (not our densenauty call), recomputes SHA-256
check_unique.sh — external-sort uniqueness of hash files

Replay of McKay on all graphs

n	graphs	full-deck collisions	reduced-deck collisions
2	2	1 (K2 ~ 2K1)	1
3	4	0	1 (P3 and K2+K1)
4–9	A000088	0	0
10	12005168	0	0

certs/n10_unique.txt plus certs/sample_n10.txt checked by verify_labelg.py.

n=14 class: degree sequence 4^11 6^3

Every such graph is a 4-regular spanning subgraph plus a triangle of non-edges (the unique 2-regular graph on the three degree-6 vertices). Generated by geng -d4 -D4 14 | add_twofactor --smin 3 --smax 3 | shortg. The degree sequence is a full-deck invariant, so uniqueness inside the class is reconstructibility.

Split graphs

Hammer–Simeone (Combinatorica 1981): split-ness is a predicate of the degree sequence, hence of the full deck. geng -S 14 produces 67,997,750 graphs. Not run to uniqueness in this folder unless certs/split14_unique.txt exists.