发表机构
Chiba Keizai University Affiliated High School（千叶经纶大学附属高中）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对沿边界相交的图，构造NBC面的相对壳化，实现Negami分裂恒等式的色特征化，并给出Gröbner基粘合公式及状态多胞体对线性块序的障碍描述。
AI 中文摘要
对于沿有限边界相交的边不相交图，我们构造了具有规定边界连通性的NBC面的相对壳化。该构造将生成森林中的路径添加到辅助有根森林复形的限制面上。当第一个图的每条边都先于第二个图的每条边时，这些相对壳化组合成一个具有连续连通性块的壳化。由此得到的h-多项式的非负分解实现了Negami分裂恒等式的色特征化。我们还给出了在大小为二或三的边界上粘合图形Orlik--Terao Gröbner基的路径公式，以及适用于任意边界的虚拟团消除公式。在树宽为二时，指数级输出下界将显式基枚举与固定树宽下的系数计算区分开来。最后，状态多胞体及其Cayley提升描述了原始坐标中线性块序的障碍以及这些序的提升实现。
英文摘要
For edge-disjoint graphs meeting along a finite boundary, we construct relative shellings of NBC faces with prescribed boundary connectivity. The construction adds paths in spanning forests to the restriction faces of auxiliary rooted-forest complexes. When every edge of the first graph precedes every edge of the second, these relative shellings combine into a shelling with consecutive connectivity blocks. The resulting nonnegative decomposition of the $h$-polynomial realizes the chromatic specialization of the Negami splitting identity. We also give path formulas for gluing graphic Orlik--Terao Gröbner bases across boundaries of size two or three, and a virtual-clique elimination formula for arbitrary boundaries. An exponential output lower bound at treewidth two distinguishes explicit basis enumeration from coefficient computation at fixed treewidth. Finally, state polytopes and their Cayley lifts describe an obstruction to linear block orders in the original coordinates and a lifted realization of these orders.
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