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− | 此词条暂由彩云小译翻译,未经人工整理和审校,带来阅读不便,请见谅。
| + | 此词条由Jie初步翻译。 |
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| [[文件:VR complex.svg|缩略图| | | [[文件:VR complex.svg|缩略图| |
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| In the mathematical area of graph theory, a clique ( or ) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent; that is, its induced subgraph is complete. Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on graphs. Cliques have also been studied in computer science: the task of finding whether there is a clique of a given size in a graph (the clique problem) is NP-complete, but despite this hardness result, many algorithms for finding cliques have been studied. | | In the mathematical area of graph theory, a clique ( or ) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent; that is, its induced subgraph is complete. Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on graphs. Cliques have also been studied in computer science: the task of finding whether there is a clique of a given size in a graph (the clique problem) is NP-complete, but despite this hardness result, many algorithms for finding cliques have been studied. |
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− | 在图论的数学领域中,团是无向图中顶点的子集,使得一个团中每两个不同的顶点必定相邻。也就是说,其导出子图是完全图。团是图论的基本概念之一,可用于图形的构建和解决许多其他数学问题。而且,在计算机科学领域中也经常会涉及到团的研究:比如在一个给定规模的图中寻找团的存在就是一个NP-完全问题。尽管我们已经明确知道这个问题很难得以解决,但仍然有许多学者在研究用于寻找团的算法。
| + | 在图论的数学领域中,'''<font color="#ff8000"> 团Clique</font>'''是无向图中顶点的子集,使得一个团中每两个不同的顶点必定相邻。也就是说,其导出子图是完全图。团是图论的基本概念之一,可用于图形的构建和解决许多其他数学问题。而且,在计算机科学领域中也经常会涉及到团的研究:比如在一个给定规模的图中寻找团的存在就是一个NP-完全问题。尽管我们已经明确知道这个问题很难得以解决,但仍然有许多学者在研究用于寻找团的算法。 |
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| A clique, C, in an undirected graph (V, E)}} is a subset of the vertices, , such that every two distinct vertices are adjacent. This is equivalent to the condition that the induced subgraph of G induced by C is a complete graph. In some cases, the term clique may also refer to the subgraph directly. | | A clique, C, in an undirected graph (V, E)}} is a subset of the vertices, , such that every two distinct vertices are adjacent. This is equivalent to the condition that the induced subgraph of G induced by C is a complete graph. In some cases, the term clique may also refer to the subgraph directly. |
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− | 在一个无向图G =(V,E)中,团C是顶点V的子集,记作:C⊆V,使得每两个不同的顶点相邻。因此团C可以看作是该无向图G的导出子集,进而将此过程视为由C引导出的完全子集的成立条件。在某些情况下,“团”这一术语也可以直接被引用为子集。
| + | 在一个无向图''G =(V,E)''中,团C是顶点V的子集,记作:''C⊆V'',使得每两个不同的顶点相邻。因此团C可以看作是该无向图G的导出子集,进而将此过程视为由C引导出的完全子集的成立条件。在某些情况下,“团”这一术语也可以直接被引用为子集。 |
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| A maximal clique is a clique that cannot be extended by including one more adjacent vertex, that is, a clique which does not exist exclusively within the vertex set of a larger clique. Some authors define cliques in a way that requires them to be maximal, and use other terminology for complete subgraphs that are not maximal. | | A maximal clique is a clique that cannot be extended by including one more adjacent vertex, that is, a clique which does not exist exclusively within the vertex set of a larger clique. Some authors define cliques in a way that requires them to be maximal, and use other terminology for complete subgraphs that are not maximal. |
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− | 极大团Maximal clique也是一个团,但是该团不能通过合并更多的相邻节点而进行扩张,换句话说,该团不可能被更大的团所包含。有些学者将“极大团”定义为“团”,而建议用其他术语来重新定义“非极大团”。 | + | '''<font color="#ff8000"> 极大团Maximal clique</font>'''也是一个团,但是该团不能通过合并更多的相邻节点而进行扩张,换句话说,该团不可能被更大的团所包含。有些学者将“极大团”定义为“团”,而建议用其他术语来重新定义“非极大团”。 |
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| The clique cover number of a graph G is the smallest number of cliques of G whose union covers the set of vertices V of the graph. | | The clique cover number of a graph G is the smallest number of cliques of G whose union covers the set of vertices V of the graph. |
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− | 图 g 的团覆盖数是 g 的团覆盖图的顶点集 v 的团的最小个数。 | + | 图 g 的'''<font color="#ff8000"> 团覆盖数Clique cover number</font>'''是 g 的团覆盖图的顶点集 v 的团的最小个数。 |
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