• Cho, Han-Hyun (Department of Mathematics Education, Seoul National University) ;
  • Kim, Suh-Ryung (Department of Mathematics, Kyung Hee University) ;
  • Nam, Yunsun (Department of Mathematics, Ewha Women’s University)
  • Published : 2000.11.01


The 2-step competition graph of D has the same vertex set as D and an edge between vertices x and y if and only if there exist (x, z)-walk of length 2 and (y, z)-walk of length 2 for some vertex z in D. The 2-step competition number of a graph G is the smallest number k such that G together with k isolated vertices is the 2-step competition graph of an acyclic digraph. Cho, et al. showed that the 2-step competition number of a path of length at least two is two. In this paper, we characterize all the minimal acyclic digraphs whose 2-step competition graphs are paths of length n with two isolated vertices and construct all such digraphs.


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