Complete Tripartite Graphs and their Competition Numbers


We present a piecewise formula for the competition numbers of the complete tripartite graphs. For positive integers x, y and z where 2 ≤ x ≤ y ≤ z, the competition number of the complete tripartite graph Kx,y,z is yz − z − y − x + 3 whenever x 6= y and yz − 2y − z + 4 otherwise. 
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