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Confirm duals 1,2 are Even Level Graphs outright; archive all six witnesses

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Tested duals 1 and 2: both are Even Level Graphs directly (dual 1 for
source 10, dual 2 for source 9), so bridge-derived with a zero-length
switch sequence. All six Holton-McKay duals are confirmed non-intertwining
(consistent with the dual-Hamiltonian theorem, since all six HM graphs are
non-Hamiltonian) and all six are bridge-derived. Saved witness files
dual_1.json, dual_2.json (0 switches) to complete the archive for all six.
Updated the n=21 subsection accordingly.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This commit is contained in:
didericis
2026-05-22 11:11:25 -04:00
parent 6f0d036e44
commit 5f6a04571c
7 changed files with 1683 additions and 8 deletions
Download Patch File Download Diff File Expand all files Collapse all files
papers/even_level_graph_generators/experiments/witnesses/dual_1.json
+495
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{
"dual_index": 1,
"n": 21,
"partition_index": null,
"labels": {
"0": 0,
"1": 0,
"2": 1,
"3": 1,
"4": 1,
"5": 0,
"6": 0,
"7": 0,
"8": 1,
"9": 0,
"10": 0,
"11": 1,
"12": 1,
"13": 0,
"14": 0,
"15": 0,
"16": 0,
"17": 0,
"18": 1,
"19": 1,
"20": 0
},
"elg_source": 10,
"elg_graph6": "T}hspWTEw`AB?J?L_CO@B??g?B??Ag?@s?AN",
"dual_graph6": "T}hspWTEw`AB?J?L_CO@B??g?B??Ag?@s?AN",
"elg_edges": [
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9,
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10,
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],
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10,
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[
11,
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],
[
11,
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],
[
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"num_bridge_switches": 0,
"bridge_switches": [],
"note": "dual is itself an Even Level Graph for this source (0 bridge switches)",
"verified": true
}
papers/even_level_graph_generators/experiments/witnesses/dual_2.json
+495
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{
"dual_index": 2,
"n": 21,
"partition_index": null,
"labels": {
"0": 0,
"1": 1,
"2": 0,
"3": 0,
"4": 1,
"5": 0,
"6": 1,
"7": 1,
"8": 0,
"9": 0,
"10": 0,
"11": 1,
"12": 1,
"13": 0,
"14": 0,
"15": 0,
"16": 0,
"17": 0,
"18": 0,
"19": 1,
"20": 1
},
"elg_source": 9,
"elg_graph6": "T}lahWYAO^@B?T?R_?o?E?@W?A_?Cg?As??n",
"dual_graph6": "T}lahWYAO^@B?T?R_?o?E?@W?A_?Cg?As??n",
"elg_edges": [
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[
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[
7,
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8,
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9,
11
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[
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12
],
[
10,
11
],
[
10,
13
],
[
11,
12
],
[
11,
13
],
[
11,
14
],
[
11,
16
],
[
12,
13
],
[
12,
14
],
[
12,
15
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[
12,
17
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[
12,
18
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[
13,
15
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[
13,
16
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[
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],
"num_bridge_switches": 0,
"bridge_switches": [],
"note": "dual is itself an Even Level Graph for this source (0 bridge switches)",
"verified": true
}