About

This site is a browseable, status-annotated index of graph-theory conjectures. It combines the graph theory category of the Open Problem Garden with conjectures extracted from recent arXiv papers by a curated set of graph theorists.

A third, small corpus holds the items of Appendix A ("Unsolved Problems") of Bondy and Murty's Graph Theory (Springer GTM 244, 2008; French edition by F. Havet, 2025) that neither of the two main corpora covered. Each such page says which nearby records exist and where in the book the item appears.

A separate automated proof-attack workstream has flagged 23 arXiv-extracted items as ill-posed in the form supplied to the model. These diagnostics are displayed alongside, and never replace, the literature-review status.

A handful of further conjectures are added by hand because they are the subject of a research workstream under problems/ in the repository but appear in none of the corpora above (source badge others); each such page links to its workstream.

The merged index contains 227 OPG problems, 768 arXiv-extracted conjectures, 38 Bondy–Murty appendix items and 1 other workstream conjecture. Each reviewed item is classified as open, partial, solved, disproved, or unclear. Separate ai-proved and ai-disproved labels identify model-generated arguments listed in the Graph-Theory-LLM-Proofs README, rated CONFIRMED, and accompanied by a linked PDF. Results rated MINOR_GAPS are excluded. The same labels mark entries whose statement is settled by a manuscript of OpenAI's collection of model-generated mathematics (released 2026-10-06); 22 entries link such a manuscript, some only as partial progress. These labels do not claim peer review. The timeline shows 130 solved or disproved conjectures as horizontal intervals from first claimed year to proof or counterexample year.

Source & licence

All problem statements, attributions, and bibliographies are reproduced from openproblemgarden.org under the GNU Free Documentation License. Each OPG problem page links back to its canonical Open Problem Garden URL. arXiv-derived records link back to their source paper via the arXiv abstract page. The project code is MIT licensed; data derived from OPG remains under the GFDL.

How it was built

• A polite Python scraper (scraper/crawl.py) walks the category listing and downloads each problem page, honouring the site's robots.txt Crawl-Delay: 10.
• scraper/parse.py turns the cached HTML into one JSON record per problem (selectors and quirks documented in PLAN.md Appendix A). Math is preserved in its LaTeX form (extracted from the alt attribute of OPG's pre-rendered TeX images).
• scraper/erdos_index.py indexes the graph-theory problems on erdosproblems.com for cross-referencing.
• scraper/intersect.py identifies likely duplicates between the two sources via citation overlap and fuzzy statement matching. Confirmed matches are surfaced as EP #N badges.
• The arXiv pipeline harvests paper metadata, downloads available HTML/PDF content, extracts conjectures, deduplicates them, and reviews each conjecture's current status.
• scripts/sync_llm_proof_results.py imports the literature resolutions, reviewed AI write-ups and ill-posed diagnostics from the separate Graph-Theory-LLM-Proofs attack corpus.
• The Bondy–Murty appendix was cross-checked item by item against the two corpora (BONDY_MURTY_APPENDIX_A.md); the uncovered items were transcribed into data/bondy_murty_conjectures.json and reviewed with the same status pipeline (scraper/bm_review.py).
• scraper/build.py renders Jinja2 templates over the JSON into the static HTML you are reading, including the merged index, per-item pages, author/tag pages, and resolved timeline. Math is typeset client-side by KaTeX.

Stats

• 1034 total index rows: 227 OPG, 768 arXiv, 38 Bondy–Murty and 1 others
• OPG review statuses: open 51partial 127ai-proved 6ai-disproved 6solved 23disproved 13unclear 1
• arXiv review statuses: open 514partial 118ai-proved 10ai-disproved 12solved 83disproved 22unclear 3
• Bondy–Murty review statuses: open 12partial 21ai-disproved 1solved 3disproved 1
• 130 solved or disproved conjectures on the resolved timeline: opg 36arxiv 90bm 4
• 437 distinct subject / keyword / author categories
• 2 cross-references to erdosproblems.com
• 23 arXiv items with an unrefereed LLM ill_posed diagnostic
• Last build: 2026-10-09

Review caveat

The status reviews are automated literature reviews with verified cited URLs. They are designed as a research aid and should be spot-checked before being used as definitive mathematical or bibliographic claims. Attack verdicts are unrefereed model self-reports. An ill-posed label is a diagnostic of the catalog statement supplied to the model, not a literature-review status or a peer-reviewed result.

Inspiration

Layout is inspired by Thomas Bloom's erdosproblems.com.