完全4-部图的交叉数

The Crossing Number of the Complete Quadruple Graph

用分情况讨论法证明了完全4-部图K_(1,1,1,n)、K_(1,1,2,n)、K_(1,1,3,n)的交叉数分别为Z(3,n)、Z(4,n)+(N/2)、Z(5,n)+n+(N/2)(n≥1).

At present, there are few results about the crossing numbers of complete quadruple graph. It was proven that the crossing number of the complete quadruple graph K_(1 ,1,1,n)、 K_(1 ,1,2,n)、 K_(1 ,1,3,n) are Z (3, n )、 Z (4, n )+ (N/2) 、 Z (5, n )+ n+(N/2)( n ≥ 1) respectively, using the classified discussions tak- ing all situations into consider.