Conjecture Fieldbook

GlossaryStudy cards

1-factorization conjecture

Source placement record

The 1-factorization conjecture that if n {\displaystyle n} {\displaystyle n} is odd or even and k ≥ n , n − 1 {\displaystyle k\geq n,n-1} {\displaystyle k\geq n,n-1}, respectively, then a k {\displaystyle k} {\displaystyle k}-regular graph with 2 n {\displaystyle 2n} {\displaystyle 2n} vertices is 1-factorable.

Review boundary: This page preserves a row from the revision-pinned source index. It is not a reviewed canonical dossier and does not independently verify or strengthen the cited claim.

Source status
Open
Field
Graph theory · Graph coloring and labeling
Record type
Revision-pinned source placement
Verification
Source-index reviewed
Source grade
secondary
Reviewed
2026-07-27T18:04:33.834Z

Context and review boundary

The source list does not provide a uniform standalone exposition for every row. Use the exact subsection and linked topic article as the starting point for a reviewed reading trail.

Formal boundary

No independent formal statement has been added to this source-index record. This prevents the catalog from inventing notation or silently strengthening the cited claim.

Known approaches and partial results

Pending review. No structured approach or partial-result note has been added to this source placement.

Source trail

  1. Wikipedia list subsection — Exact Graph theory › Graph coloring and labeling subsection in the revision-pinned source.
  2. Wikipedia topic article — Background article linked by the source index; follow its references for deeper study.
  3. Pinned source revision 1366281547 — Revision-pinned snapshot from 7/27/2026.