Document Type
Lecture
Publication Date
4-20-2012
Abstract
Let G be a simple graph and let Ik denote the graph on k isolated vertices. The competition number of G is the minimum k such that G Ik is the competition graph of an acyclic digraph. 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 Kxy z is yz z y x + 3 whenever x= y and yz 2y z+4otherwise. Wealso present bounds for the competition number of Knnnn when n is odd.
Relational Format
presentation
Recommended Citation
Kuhl, Jaromy, "Complete tripartite graphs and their competition numbers" (2012). Combinatorics Seminar. 62.
https://egrove.olemiss.edu/math_combinatorics/62
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