arXiv:2611.16839 · v1

An upper bound on the number of edges of a Gomory corner polyhedron

首次提交 2026-11-12 22:17

版本更新 2026-11-12 22:17

雷达观测 2026-11-13 14:15

摘要

We establish the first nontrivial upper bound on the number of edges of a Gomory corner polyhedron, resolving a long-standing open question. For an $n$-dimensional corner polyhedron associated with an integer lattice of determinant $δ$, the number of edges is at most $$O\left(n6^n \cdot \bigl(1+\log_2(2δ)\bigr)^{2n-3}\right).$$ This improves the standard bound obtained by counting pairs of vertices, reducing the logarithmic exponent from $(2n-2)$ to $(2n-3)$.