{ "experiment": "hn_spectral_database", "timestamp": "2026-07-04T15:01:00Z", "include_degrey": true, "graphs": [ { "description": "Moser spindle", "n_vertices": 7, "n_edges": 12, "lambda_max": 3.645751311065, "lambda_min": -2.0, "hoffman_bound": 2.822875655532, "chi_hoffman": 3, "welch_wynn": 2.086905488878, "chi_welch_wynn": 3, "best_spectral_lower_bound": 3, "chi_known": 4, "gap": "gap=1" }, { "description": "Golomb graph (8 vertices, 10 edges)", "n_vertices": 8, "n_edges": 10, "lambda_max": 2.681330643605, "lambda_min": -2.323404276086, "hoffman_bound": 2.154052556071, "chi_hoffman": 3, "welch_wynn": 1.504135614368, "chi_welch_wynn": 2, "best_spectral_lower_bound": 3, "chi_known": 4, "gap": "gap=1" }, { "description": "Empty graph (10v baseline)", "n_vertices": 10, "n_edges": 0, "lambda_max": 0.0, "lambda_min": 0.0, "hoffman_bound": null, "chi_hoffman": null, "welch_wynn": 1.0, "chi_welch_wynn": 1, "best_spectral_lower_bound": 1, "chi_known": 1, "gap": "tight" }, { "description": "Path graph P10 (baseline)", "n_vertices": 10, "n_edges": 9, "lambda_max": 1.918985947229, "lambda_min": -1.918985947229, "hoffman_bound": 2.0, "chi_hoffman": 2, "welch_wynn": 1.237468458129, "chi_welch_wynn": 2, "best_spectral_lower_bound": 2, "chi_known": 2, "gap": "tight" }, { "description": "Cycle C5 (baseline)", "n_vertices": 5, "n_edges": 5, "lambda_max": 2.0, "lambda_min": -1.61803398875, "hoffman_bound": 2.2360679775, "chi_hoffman": 3, "welch_wynn": 1.666666666667, "chi_welch_wynn": 2, "best_spectral_lower_bound": 3, "chi_known": 3, "gap": "tight" }, { "description": "Complete K4 (baseline)", "n_vertices": 4, "n_edges": 6, "lambda_max": 3.0, "lambda_min": -1.0, "hoffman_bound": 4.0, "chi_hoffman": 4, "welch_wynn": 4.0, "chi_welch_wynn": 4, "best_spectral_lower_bound": 4, "chi_known": 4, "gap": "tight" }, { "description": "De Grey G (1581 vertices, 7877 edges)", "n_vertices": 1581, "n_edges": 7877, "lambda_max": 12.091766719308, "lambda_min": -7.73894638212, "hoffman_bound": 2.562456453665, "chi_hoffman": 3, "welch_wynn": null, "chi_welch_wynn": null, "best_spectral_lower_bound": 3, "chi_known": 5, "gap": "gap=2" }, { "description": "de Grey subgraph (n=50, e=100)", "n_vertices": 50, "n_edges": 100, "lambda_max": 5.866375245109, "lambda_min": -4.056427910215, "hoffman_bound": 2.446192407447, "chi_hoffman": 3, "welch_wynn": 1.132923032669, "chi_welch_wynn": 2, "best_spectral_lower_bound": 3, "chi_known": null, "gap": "?" }, { "description": "de Grey subgraph (n=100, e=266)", "n_vertices": 100, "n_edges": 266, "lambda_max": 7.080506734483, "lambda_min": -4.563418201316, "hoffman_bound": 2.551579632224, "chi_hoffman": 3, "welch_wynn": null, "chi_welch_wynn": null, "best_spectral_lower_bound": 3, "chi_known": null, "gap": "?" }, { "description": "de Grey subgraph (n=200, e=747)", "n_vertices": 200, "n_edges": 747, "lambda_max": 9.241919119832, "lambda_min": -5.218824047335, "hoffman_bound": 2.770881531166, "chi_hoffman": 3, "welch_wynn": null, "chi_welch_wynn": null, "best_spectral_lower_bound": 3, "chi_known": null, "gap": "?" }, { "description": "de Grey subgraph (n=500, e=2242)", "n_vertices": 500, "n_edges": 2242, "lambda_max": 11.690329949761, "lambda_min": -7.523976221726, "hoffman_bound": 2.553743606473, "chi_hoffman": 3, "welch_wynn": null, "chi_welch_wynn": null, "best_spectral_lower_bound": 3, "chi_known": null, "gap": "?" } ], "sha256": "2041b3ce8902f73ae8b92f1696b6badbd69718d30304c78dfa61ec67b5e270c1" }