Test: Chromatic Number Bounds for Random Graphs (GMD-T1)

**Problem**: Prove tighter bounds on the chromatic number of Erdős–Rényi random graphs G(n,p) in the regime p = c/n for c near the colorability threshold.

**Why good test**: Requires probabilistic method, second moment method, known literature (Achlioptas, Naor). Tests counterexample search, convergence verification, and special case checking.

**Domain**: Combinatorics / Probabilistic Method
**Expected difficulty**: Medium

Start by formalizing the Erdős–Rényi G(n,p) setting for p = c/n near the colorability threshold, then review the probabilistic and second moment methods in the cited Achlioptas and Naor literature. Done means a rigorous proof of tighter chromatic-number bounds, with counterexamples, convergence, and special cases checked.

Written by the indexing model from the issue text.