K(n,m)图的边色数

On The Edge Chromatic Number of K (n, m)

设K(n,0)=Kn,V(Kn)={v_1～0,v_2～0…,v_n～0},分别从v_1～0,v_2～0,…,v_(n-1)～0,出发作长为m的n-1条路v_i～0,v_i～1,…,v_i～m,i=1,2,…,n-1;然后,对j=1,2,…,m,添加边{v_i～jv_k～j|k,i=1,2,…,n-1,且k≠i},这样得到的图用K(n,m)表示.证明了对图K(n,m)当n≥2、m≥1时的边色数为n.

Supposing K(n ,0) = Kn, and V(kn) = { v_1~0,v_2~0,…,V_n^0}, and v-i^0, v_i^1,…,v_i^m are paths(i = 1,2,…, n - 1) ;, and{v_i^j v_k^j} k = 2,3,…, n - 1, i = 1,2, …, n -2,k > i; and { j = 1,2, …, m } this graph is defined k (n , m ) In this paper, we proved on the chromatic number of graph K(n ,m), (with n≥2,m ≥1) is n.