Combinatorics · Oct 6, 2026
Correspondence coloring with a fixed forbidden subgraph
Proves the Alon–Krivelevich–Sudakov coloring conjecture in correspondence-coloring form: graphs avoiding any fixed subgraph F need colors when their maximum degree Δ is sufficiently large. Also proves the Ajtai–Erdős–Komlós–Szemerédi independence conjecture: for fixed r ≥ 4, every n-vertex Kr-free graph of average degree d ≥ 2 has an independent set of size .
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