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Let φ be a symmetric function defined from N×N into N, where N denotes the nonnegative integers. A graph G=(V,E) is a φ-tolerance competition graph if there is a digraph D=(V,A) such that each vertex vi∈V can be assigned a nonnegative integer ti such that, for i≠j, vivj∈E if and only if |O(vi)∩O(vj)|≥φ(ti,tj). Brigham et al. defined the two-φ-tolerance competition graph as a tolerance competition...
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