Hamilton Starters and Path Decompositions in Directed Circulants

What the math gives to ML

The paper gives an explicit decomposition of a dense directed circulant graph into Hamilton cycles and, after coordinated edge deletion, into only r+1 directed paths. The transferable asset is not merely graph factorization, but exact coverage of every local offset edge together with long ordered traversals that can be executed as scans. This suggests a deterministic sparse token-mixing or graph-neural layer that replaces irregular offset aggregation with a small set of reusable path scans, potentially improving kernel fusion and memory locality. The first experiment should compare path-ordered aggregation with explicit local attention at equal edge count and parameter count.