Corrupted Graph-Theory Contents Fragment

Definitions and mathematical statement

Unrecoverable mathematical statement. The supplied record is titled "Corrupted Graph-Theory Contents Fragment" and has statement_status: unrecoverable. Its statement and original-statement fields contain a damaged table-of-contents fragment listing several workshop contributions, rather than mathematical definitions, hypotheses, or a conjecture. The clean-statement field is empty. Consequently, no precise mathematical assertion, domain, boundary conditions, or quantifiers can be recovered from the supplied evidence.

One listed contribution is "Rainbow triangles and the Erdős--Hajnal problem in projective geometries," attributed in the fragment to Peter Nelson, jointly with Carolyn Chun, James Dylan Douthitt, Wayne Ge, Tony Huynh, and Matthew E. Kroeker, with page reference 46. This title does not specify the intended mathematical problem or justify identifying it with a particular graph-theoretic or projective-geometric formulation of an Erdős--Hajnal problem. No such formulation is asserted here.

The supplied verification field reports that the official report identifies this extraction as a damaged contents listing, and that no separate clean statement has been promoted; the original record is retained for provenance. This is a supplied verification assertion, not an independent source check. The record's separate label partially_solved and its dated literature assessment do not resolve the missing mathematical target.

Short English statement

The supplied text is a corrupted workshop contents listing. It provides no recoverable mathematical problem, so a precise statement requires human review of the underlying report. The supplied partially solved label and Erdős--Hajnal literature assessment cannot be assigned to a uniquely identified conjecture from this fragment.

Sources

• Local UnsolvedMath registry, supplied record with permanent ID $30006142$, exact source problem code catalogue entry, title "Corrupted Graph-Theory Contents Fragment," in the collection "Oberwolfach Reports Open Problems." The proposed-year field is 2025; no proposer is supplied. The record was updated at 2026-09-16T12:06:53Z. Its supplied verification describes an unrecoverable contents-listing extraction retained for provenance.
• Supplied report citation: Graph Theory (2025), Oberwolfach Reports, pp. 5--74, DOI 10.4171/owr/2025/1. https://doi.org/10.4171/owr/2025/1. The supplied background describes Oberwolfach Reports as documenting mathematical workshops and their open-problem discussions; that general description does not establish a mathematical statement for this extraction.
• Attribution appearing in the fragment: Peter Nelson, jointly with Carolyn Chun, James Dylan Douthitt, Wayne Ge, Tony Huynh, and Matthew E. Kroeker, "Rainbow triangles and the Erdős--Hajnal problem in projective geometries," page reference 46. This attributes a listed contribution, not a recovered conjecture or its proposer.
• Supplied literature source: "Nguyen--Scott--Seymour, Proc. LMS 2026." https://doi.org/10.1112/plms.70133.
• Supplied literature source: "OWR 2025/1." https://ems.press/content/serial-article-files/51346.
• Supplied literature assessment, checked on exactly 2026-08-22: the record labels the problem partially solved and states that the extracted Erdős--Hajnal problem remains open in general, with substantial special cases known, including completion of all five-vertex cases in 2026. This is supplied dated curation derived from the OWR curation, not independently verified here. Its time-sensitive status and cited claims require independent verification, and its applicability to this damaged extraction remains unresolved.