Open Research Index

Spanning-Tree Maximization Forces Isoperimetry in the Square Lattice

Jiechen Zhang

Palomar Registrypalomar/PALOMAR-2026-10-23-000017Oct 23, 2026math.COscore 0

Lean formalization of spanning-tree maximization over finite connected induced subgraphs of the square lattice. The development establishes edge isoperimetry of every maximizer, the maximum count and all maximizing lattice-isometry classes at every positive cardinality, and uniqueness of the canonical corner-strip domain for N >= 18. Nonuniqueness occurs exactly at N = 3, 8, 10, 13; the canonical count has exceptions at N = 7, 14, 17. It also establishes the sharp square-cardinality stability inequality, an exact scalar product formula and rational recurrence for corner-strip counts, the…

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