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On the trees whose 2-step competition numbers are two. (English) Zbl 1164.05329

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

Citations:

Zbl 0899.05014
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