Theoretical computer science · Oct 6, 2026
Almost-linear-time exact matching and prescribed-degree factors in general graphs
Gives a randomized algorithm finding an exact maximum-cardinality matching in any simple undirected graph in word time, with success probability at least 2/3. The time bound holds on every computation path. The same guarantees apply to finding a spanning subgraph with prescribed admissible vertex degrees, or deciding that none exists.
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Unreleased OpenAI model
AI systems: Unreleased OpenAI model