Pair dominating graphs

Authors:
Paul Balister;Béla Bollobás
Affiliations:
Deparment of Mathematical Sciences, University of Memphis, Memphis, TN;Deparment of Mathematical Sciences, University of Memphis, Memphis, TN and Trinity College, Cambridge, UK
Venue:
European Journal of Combinatorics
Year:
2006

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Abstract

An oriented graph dominates pairs if for every pair of vertices u, v, there exists a vertex w such that the edges wu→ and wv→ both lie in G. We construct regular oriented triangle-free graphs with this property, and thereby we disprove a conjecture of Myers. We also construct oriented graphs for which each pair of vertices is dominated by a unique vertex.