ORTHOGONAL REPRESENTATIONS AND CONNECTIVITY OF GRAPHS
ORTHOGONAL REPRESENTATIONS AND CONNECTIVITY OF GRAPHS
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DOI：
10.1016/0024-3795(89)90475-8
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发表时间：
1989-03-01
影响因子：
1.1
通讯作者：
SCHRIJVER, A
中科院分区：
文献类型：
--
作者：
LOVASZ, L;SAKS, M;SCHRIJVER, A
证明了n个结点的图是k-连通的当且仅当它的结点可以用维数为k的真实的向量表示，使得（a）不相邻的结点用正交向量表示，（B）任意k个结点线性无关.证明了具有性质（a）和（B）的所有表示的集合的闭包不可约为代数簇，并研究了具有性质（a）的所有表示的簇的不可约性问题.
It is proved that a graph onnnodes isk-connected if and only if its nodes can be represented by real vectors in dimensionn–ksuch that (a) nonadjacent nodes are represented by orthogonal vectors and (b) anyn–kof them are linearly independent. We show that the closure of the set of all representations with properties (a) and (b) is irreducible as an algebraic variety, and study the question of irreducibility of the variety of all representations with property (a).