The spliting number of a graph G is the smallest integer k > 0 such that a planar graph can be obtained from G by k splitting operations. Such operation replaces v by two nonadjacent vertices V sub 1 and v sub 2, and attaches the neighbors of v either ot v sub 1 or to v sub 2. The n-cube has a distinguished place in computer science. Dean and Richter devoted an article to proving that the minimum numberof crossings in an optimum drawing of the 4-cube is 8, but no results about splitting number of other nonplanar n-cubes are known. In this note we give a proof that the splitting number of the 4-cube is 4. In addition, we give the lower bound 2 sup n-2 for the splitting number of the n-cube. It is known that the splitting number of the n-cube is O(2 sup n), thus our results that the splitting number of the n-cube is sita(2 sup n).
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机译：图G的分割数是k> 0的最小整数，因此可以通过k次分割操作从G获得平面图。这样的操作用两个不相邻的顶点V sub 1和v sub 2替换v，并将v的相邻对象附加到v sub 1或v sub2。n立方体在计算机科学中具有显着的地位。迪恩和里希特（Dean and Richter）专心致志地证明，在4角立方体的最佳绘图中，最小的相交数目是8，但是尚无关于分裂其他非平面n角立方体的结果的信息。在此注释中，我们提供了一个证明4多维数据集的分割数为4。此外，我们给出了n多维数据集的分割数的下界2 sup n-2。已知n立方体的分裂数为O（2 sup n），因此我们的结果为n立方体的分裂数为sita（2 sup n）。
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