OJMath Publishes Landmark Resolution of the Hadwiger–Nelson Problem on Infinite Graphs
Onyx Press is pleased to announce that the Onyx Journal of Mathematics (OJMath) has published a landmark resolution of the Hadwiger–Nelson problem restricted to infinite unit-distance graphs over the rational plane. The paper, authored by an international consortium led by Dr. Imre Varga (Budapest University of Technology) and Dr. Sofia Marchetti (Scuola Normale Superiore di Pisa), establishes that the chromatic number of the rational plane is exactly 6 — a single-unit improvement over the long-standing upper bound of 7.
The proof combines classical Ramsey-theoretic arguments with modern computational enumeration of critical subgraphs. By restricting attention to rational coordinates, the authors circumvent the independence obstacles that have stalled progress on the full real-plane problem since the de Grey (2018) breakthrough. The construction also yields the first explicit 6-chromatic unit-distance graph with rational coordinates, comprising 1,583 vertices and 7,461 edges.
All datasets, source code, and the complete enumeration log have been deposited in the Onyx Press open repository under a CC-BY 4.0 licence. Three independent referees confirmed the computational steps using verified Lean 4 proof-assistant translations. The article is available immediately at math.onyx-press.org with no embargo and is fully citable via its DOI.