p-competition graphs

Dedicated to Professor John Maybee on the occasion of his 65th birthday.
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Abstract

If D = (V, A) is a digraph, its p-competition graph has vertex set V and an edge between x and y if and only if there are distinct vertices a1, …, ap and arcs (x, ai) and (y, ai) in D for each ip. This definition generalizes the widely studied p = 1 case of ordinary competition graphs. We obtain results about p-competition graphs analogous to the well-known results about ordinary competition graphs and apply these results to specific cases.

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