Cho, Han Hyuk; Kim, Suh-Ryung; Nam, Yunsun On the trees whose 2-step competition numbers are two. (English) Zbl 1164.05329 Ars Comb. 77, 129-142 (2005). Summary: Since J.E.Cohen introduced the notion of competition graph in 1968, numerous variations have been defined and studied by several authors.H.H.Cho, S.-R.Kim and Y.Nam [Congr.Numerantium 123, 43-53 (1997; Zbl 0899.05014)] gave a sufficient condition for a tree to have the 2-step competition number two. In this paper, we show that this sufficient condition is also a necessary condition for a tree to have the 2-step competition number two, which completely characterizes the trees of that kind. In fact, this result turns out to characterize the connected triangle-free graphs whose 2-step competition numbers are two. MSC: 05C05 Trees Keywords:2-step competition graph; trees; triangle-free graphs Citations:Zbl 0899.05014 PDFBibTeX XMLCite \textit{H. H. Cho} et al., Ars Comb. 77, 129--142 (2005; Zbl 1164.05329)