Open Research Index

Regular subgraphs of almost regular graphs (Alon–Friedland–Kalai)

Juan Pablo Traverso Gianini

Palomar Registrypalomar/PALOMAR-2026-10-26-000001Oct 26, 2026math.COscore 0

A Lean 4 / Mathlib formalization of the Alon–Friedland–Kalai theorem for primes: for a prime p, every finite simple graph with maximum degree at most 2p − 1 and average degree greater than 2p − 2 contains a p-regular subgraph (a nonempty subgraph with all degrees 0 or p); as a corollary, every 4-regular graph plus an edge contains a 3-regular subgraph. The prime-power case of the paper is not stated. The proof uses Mathlib's Chevalley–Warning theorem.

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