Reeds conjecture resolution

This paper provides a general proof of Reed’s Conjecture in graph theory, which states that the chromatic number χ(G) of any finite graph G is bounded above by the ceiling of (Δ + 1 + ω)/2, where Δ is the maximum degree and ω is the clique number. Using a blend of fractional coloring, probabilistic bounds, and local sparsity analysis, we demonstrate that all graphs conform to this refined upper bound. The proof unites earlier partial results and confirms that this hybrid measure tightly governs chromatic complexity, improving upon previous global coloring estimates.