The complexity of cubical graphs

Q4 Mathematics 信息与控制 Pub Date : 1985-07-01 DOI:10.1016/S0019-9958(85)80012-7
Foto Afrati, Christos H. Papadimitriou , George Papageorgiou
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引用次数: 23

Abstract

A graph is cubical if it is a subgraph of a hypercube; the dimension of the smallest such hypercube is the dimension of the graph. We show several results concerning this class of graphs. We use a characterization of cubical graphs in terms of edge coloring to show that the dimension of biconnected cubical graphs is at most half the number of nodes. We also show that telling whether a graph is cubical is NP-complete. Finally, we propose a heuristic for minimizing the dimension of trees, which yields an embedding of the tree in a hypercube of dimension at most the square of the true dimension of the tree.

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三次图的复杂性
如果一个图是超立方体的子图,那么它就是立方图;最小的超立方体的维数就是图的维数。我们给出了关于这类图的几个结果。我们利用三次图的边缘着色表征,证明了双连通三次图的维数最多是节点数的一半。我们还证明了判断一个图是否是三次图是np完全的。最后,我们提出了一种最小化树的维度的启发式方法,该方法产生了树在维度最多为树的真实维度的平方的超立方体中的嵌入。
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来源期刊
信息与控制
信息与控制 Mathematics-Control and Optimization
CiteScore
1.50
自引率
0.00%
发文量
4623
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