Colorability of stress-free diameter frameworks

Prove or disprove Kalai's conjecture that every stress-free diameter framework in R^d is (d+1)-colorable.

Background

The paper places this conjecture in the context of higher-dimensional diameter graphs and Borsuk-type coloring questions. It proposes that stress-freeness may impose enough combinatorial structure to guarantee a coloring with d+1 colors, potentially providing a route toward weakened forms of Borsuk's conjecture.

References

If $G$ is a stress-free diameter framework in $Rd$ then $G$ is $(d+1)$-colorable.

— Geometric Realizations with Strong Self-Duality Part II: Diameter Graphs, Reuleaux Polyhedra, and Thrackles  (2610.06340 - Damásdi, 5 Oct 2026) in Section 12, subsection “Stress-free diameter frameworks in higher dimensions,” Kalai conjecture