超细胞图：没有$Q_3^-$作为部分立方体子图的部分立方体
Hypercellular graphs: partial cubes without $Q_3^-$ as partial cube minor
摘要：
我们研究了超立方体的等距子图的结构（即，部分立方体），其不包含可收缩到3-立方体减去一个顶点$Q^-_3$的有限凸子图（这里收缩意味着收缩对应于超立方体的相同坐标的边）。推广了中值图和细胞图的类似结果，证明了这种图的等距圈的凸包是门控的，并且同构于边和偶圈的笛卡儿积。此外，我们证明了我们的图正是部分立方体类，其中任何有限的凸子图都可以通过连续的门汞齐从边和甚至圈的笛卡儿积得到。这个分解结果使我们能够建立各种结果。特别是，它产生，我们的类图推广中位数和细胞图，这激发命名我们的图超细胞。此外，我们还证明了超胞图是定向拟阵的带蛋白石复形的拓扑图。最后，我们将超细胞图的特征描述为中值细胞-一个自然推广中值图概念的属性。
英文摘要：
We investigate the structure of isometric subgraphs of hypercubes (i.e., partial cubes) which do not contain finite convex subgraphs contractible to the 3-cube minus one vertex $Q^-_3$ (here contraction means contracting the edges corresponding to the same coordinate of the hypercube). Extending similar results for median and cellular graphs, we show that the convex hull of an isometric cycle of such a graph is gated and isomorphic to the Cartesian product of edges and even cycles. Furthermore, we show that our graphs are exactly the class of partial cubes in which any finite convex subgraph can be obtained from the Cartesian products of edges and even cycles via successive gated amalgams. This decomposition result enables us to establish a variety of results. In particular, it yields that our class of graphs generalizes median and cellular graphs, which motivates naming our graphs hypercellular. Furthermore, we show that hypercellular graphs are tope graphs of zonotopal complexes of oriented matroids. Finally, we characterize hypercellular graphs as being median-cell -- a property naturally generalizing the notion of median graphs.
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