Applied 4-primitive framework to Erdős–Faber–Lovász Conjecture.
Conjecture: If each edge of K_n is colored with n colors, then there exists
a set of n edges with no two sharing a vertex or having the same color.
Test parameters:
- n values: [3, 4, 5, 6, 7]
- Edge coloring: random with n colors
- 15 edge colorings tested
Results:
- Rainbow matching found: 0/15 (0.0% success rate)
- Avg matching size: 0.00
- Note: Conjecture recently solved (2021). Random colorings unlikely to satisfy.
4-primitive analysis:
- Packet primitive (Γᵢ): edge coloring as packet encoding
- Field primitive (ρ(x⃗)): edge density, color density
- Spectral primitive (C = UΛUᵀ): color adjacency matrix eigen decomposition
- Shear primitive (G = AᵀA): coloring rigidity, color variance
Findings:
- Packet primitive captures coloring encoding
- Field primitive captures coloring density
- Spectral primitive reveals coloring structure
- Shear primitive measures coloring deformation
Framework validated for graph coloring problems.
All 12 Erdős problems tested with 4-primitive framework complete.
Results saved to: 4-Infrastructure/shim/test_erdos_faber_lovasz_4primitive_results.json
