虚拟图与柄体链环的桥数
Bridge numbers of virtual graphs and handlebody-links
中文总结 AI 辅助
本文研究图、虚拟图及柄体类的桥指标，构造虚拟ravel等例子，证明多种桥指标差异无界，并给出Suzuki曲线边连通和的精确指标。
中文摘要 AI 辅助
我们研究了图、虚拟图及其柄体类的桥指标。我们构造了虚拟ravel，使得桥指标与加权上跨桥指标之差无界。下界利用$\u005a_2$-双quandle族中一个固定流的指数多个着色。对于每个负欧拉示性数，我们构造了具有任意大桥指标的固定三叉图的经典几乎未打结图。我们还获得了每个固定花束秩的ravel的无界偶数桥指标。另一个几乎未打结族具有其空间图桥指标与其正则邻域桥指标之间的无界差。最后，Suzuki曲线的边连通和给出了精确的约束和无约束桥指标，其差无界。
英文摘要
We study bridge indices of graphs, virtual graphs, and their handlebody classes. We construct virtual ravels for which the difference between bridge index and weighted overpass bridge index is unbounded. The lower bound uses exponentially many colorings for one fixed flow in a $\Z_2$-family of biquandles. For each negative Euler characteristic we construct classical almost unknotted graphs of one fixed trivalent graph with arbitrarily large bridge index. We also obtain unbounded even bridge indices for ravels of each fixed bouquet rank. A separate almost unknotted family has an unbounded difference between its spatial-graph bridge index and the bridge index of its regular neighborhood. Finally, edge connected sums of Suzuki curves give exact constrained and unconstrained bridge indices whose difference is unbounded.
