Results¶
Each section below gives the nontrivial-survivor count, links to the corresponding census file in the public repository, and the gallery image rendered from that file. For orders with many survivors the gallery shows a representative sample; the panel title records how many of the total are displayed.
The Interactive explorer provides a browser-based entry point for browsing the same census.
Order 9¶
- Nontrivial survivors: 1
- Census file:
order_9_delta_3.json - Explorer: Interactive explorer
Order 11¶
- Nontrivial survivors: 2
- Census file:
order_11_delta_3.json - Explorer: Interactive explorer
Order 13¶
- Nontrivial survivors: 14
- Census file:
order_13_delta_3.json - Explorer: Interactive explorer
Order 15¶
- Nontrivial survivors: 94
- Census file:
order_15_delta_3.json - Explorer: Interactive explorer
Order 17¶
- Nontrivial survivors: 774
- Census file:
order_17_delta_3.json - Explorer: Interactive explorer
Order 19¶
- Nontrivial survivors: 6,984
- Census file:
order_19_delta_3.json.gz - Explorer: Interactive explorer
Order 21¶
- Nontrivial survivors: 70,530
- Census file:
order_21_delta_3.json.gz - Explorer: Interactive explorer
Order 22¶
- Nontrivial survivors: 1
- Census file:
order_22_delta_3.json.gz - Explorer: Interactive explorer
Order 23¶
- Nontrivial survivors: 782,186
- Census file:
order_23_delta_3.json.gz - Explorer: Interactive explorer (200-survivor sample)
- Characterization clause counts: (a) vertex-blowup 672,397 · (b) Hajós-join 71,812 · (c) Meredith-type 11,260 · (d) snark-completion 26,717 · (e) 0 — sum-check passes.
Order 24¶
- Nontrivial survivors: 9
- Census file:
order_24_delta_3.json.gz - Explorer: Interactive explorer
- Structure: eight contractible-triangle blowups of the unique order-22 survivor; one triangle-free primitive graph.
Even-order milestones¶
The gallery below places the unique order-22 survivor beside all nine order-24 survivors. Orange vertices have degree 2; the highlighted fifth order-24 graph is the triangle-free primitive case.
