带面体图的刻画
Characterizing Graphs of Zonohedra
摘要：
Steinitz的一个经典定理指出，一个图G可由一个凸多面体实现当且仅当G是3-连通平面图。带面体是凸多面体的一个重要子类，具有带面体的面是平行四边形并且是平行对的性质。本文给出了带面体图的刻划。我们也给出了一个线性时间算法来识别这样的图。在我们寻找算法的过程中，我们证明了在一个带面体P中，区域数和每个区域中的面数都是O（平方根{n}），其中n是P的顶点数。
英文摘要：
A classic theorem by Steinitz states that a graph G is realizable by a convex polyhedron if and only if G is 3-connected planar. Zonohedra are an important subclass of convex polyhedra having the property that the faces of a zonohedron are parallelograms and are in parallel pairs. In this paper we give characterization of graphs of zonohedra. We also give a linear time algorithm to recognize such a graph. In our quest for finding the algorithm, we prove that in a zonohedron P both the number of zones and the number of faces in each zone is O(square root{n}), where n is the number of vertices of P.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
