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$$p$$-competition graphs. (English) Zbl 0824.05027
The $$p$$-competition graph of a digraph $$D= (V, A)$$ is the graph with vertex set $$V$$ and an edge between $$x$$ and $$y$$ whenever there exist distinct vertices $$v_ 1, v_ 2,\dots, v_ p$$ and arcs $$(x, v_ i)$$, $$(y,v_ i)$$ in $$D$$ for each $$i\leq p$$. In case $$p= 1$$ the concept coincides with the competition graph which has received a great deal of attention in the literature since being introduced by J. E. Cohen in 1968, see, e.g., R. D. Dutton and R. C. Brigham [A characterization of competition graphs, Discrete Appl. Math. 6, 315-317 (1983; Zbl 0521.05057)]. In the present paper, the authors study properties of $$p$$-competition graphs, obtaining, where possible, analogues of results about ordinary competition graphs.

##### MSC:
 05C20 Directed graphs (digraphs), tournaments
##### Keywords:
digraph; competition graph
Full Text:
##### References:
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