The Erdős–Gallai cycle-decomposition conjecture
What the paper claims, in its own words
Proves that the edges of every finite simple undirected graph on n vertices can be partitioned into at most simple cycles and single edges, for an absolute constant C. This resolves the Erdős–Gallai cycle-decomposition conjecture, bounding the number of pieces linearly even for dense graphs.
The plain-language explainer for this entry is still coming.
The original paper
- A linear cycle-and-edge decomposition of every graph (PDF, opens in a new tab) September 24, 2026 Formal proof listed