完全三部图K_(n_1,n_2,n_3)的竞赛数

The competition numbers of complete tetrapartite graphs K_(n_1,n_2,n_3)

对于一个图G,一般情况下计算它的竞赛数k(G)是很困难的。本文给出了关于完全三部图Kn1,n2,n3(n1≥n2≥n3≥2)的边团覆盖数和竞赛数:θe(Kn1,n2,n3)=n1n2 k(Kn1,n2,n3)={n1n2-n1-n2-n3+4 n1≥n2=n3 n1n2-n1-n2-n3+3 n1≥n2>

For a graph G,it is known to be a hard problem to compute the competition number k（G） of the graph G in general.In this paper,it is given that the results about the edge clique cover number and the competition number of complete tripartite graph Kn1,n2,n3（n1≥n2≥n3≥2） as follows：θe（Kn1,n2,n3）=n1n2k（Kn1,n2,n3）={n1n2-n1-n2-n3＋4, n1≥n2=n3;n1n2-n1-n2-n3＋3,n1≥n2〉n3