On the crossing numbers of W_6×S_n
Jing Wang · 2013
In the early 1950s,Zarankiewicz conjectured that the crossing number of the complete partite graph K_(m,n)(m≤n) is[m/2][(m-1)/2][n/2][(n-1)/2](for any real number x,[x]denotes the maximum integer that is no more than x).At present,the truth of this conjecture has been proved for the case m≤6.This paper determines the crossing number of the Cartesian product W_6 with S_n is cr(W_6×S_n)=9[n/2][(n-1)/2]+2n+5[n/2],provided that Zarankiewicz's conjecture holds for the case m=7.