Local Separators in Large Networks

Definitions and mathematical statement

Recorded prompt. "What are local separators of large networks? The report passage is retained verbatim as the relevant context for this extracted problem."

Definitions and formulation limitations. The supplied record does not reproduce a definition of a local separator, specify a class of networks, quantify what constitutes a large network, or state a property to be proved. Consequently, no precise mathematical assertion or quantified research problem can be recovered from the supplied text without introducing unsupported assumptions.

The supplied statement-verification note reports that the official report immediately answers this rhetorical heading by defining local separators and that the heading is therefore not an open problem. That definition and the surrounding report passage are absent from the supplied record. The statement is marked unrecoverable, and no clean statement is supplied. This draft preserves the recorded prompt for provenance; it does not promote it to a conjecture or supply a substitute definition.

The registry nevertheless labels the entry open. Its supplied literature assessment treats the text as a broad research prompt with no unique theorem whose truth would constitute a resolution, and labels it open under an uncertainty rule. These supplied classifications do not establish a well-defined open mathematical problem.

Short English statement

The record asks what local separators of large networks are, but supplies neither their definition nor a precise mathematical question. Its verification note identifies the wording as a rhetorical heading answered in the report, while the registry retains an open label. Recovering the actual passage is necessary before a mathematical statement can be prepared.

Sources

• Supplied local UnsolvedMath registry record, permanent ID $30004959$, title Local Separators in Large Networks, exact source problem code catalogue entry; collection: Oberwolfach Reports Open Problems. No individual proposer is supplied; the recorded proposed year is 2022.
• Supplied report citation: Graph Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/1, pp. 5--78. Supplied source link: https://doi.org/10.4171/owr/2022/1. The background attributes the material to mathematical workshop reports and their open-problem discussions; this general provenance does not establish that this particular heading is an open problem.
• Supplied literature source, labelled "original OWR report": https://doi.org/10.4171/OWR/2022/1.
• Literature assessment dated exactly 2026-08-22: supplied dated curation, not independently verified. It labels the entry open under an uncertainty rule because the extracted research prompt specifies no unique resolution criterion. The supplied background requests independent verification of time-sensitive status and cited claims.
• Supplied statement-verification note: the official report answers the rhetorical heading by defining local separators; no separate clean statement is promoted, and the original record remains publicly visible for provenance. This is a supplied verification claim, not an independent examination of the report. The record was updated on 2026-09-16.