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The elimination procedure for the competition number is not optimal
2006
Discrete Applied Mathematics
Given an acyclic digraph D, the competition graph C(D) is defined to be the undirected graph with V (D) as its vertex set and where vertices x and y are adjacent if there exists another vertex z such that the arcs (x, z) and (y, z) are both present in D. The competition number k(G) for an undirected graph G is the least number r such that there exists an acyclic digraph F on |V (G)| + r vertices where C(F ) is G along with r isolated vertices. Kim and Roberts [The Elimination Procedure for the
doi:10.1016/j.dam.2005.11.009
fatcat:z4dpj7eac5gcreghdq6iolhrea