Abstract
For a finite poset P = (V, ≤ ), let \({\cal B}_s(P)\) consist of all triples (x,y,z) ∈ V 3 such that either x < y < z or z < y < x. Similarly, for every finite, simple, and undirected graph G = (V,E), let \({\cal B}_s(G)\) consist of all triples (x,y,z) ∈ V 3 such that y is an internal vertex on an induced path in G between x and z. The ternary relations \({\cal B}_s(P)\) and \({\cal B}_s(G)\) are well-known examples of so-called strict betweennesses. We characterize the pairs (P,G) of posets P and graphs G on the same ground set V which induce the same strict betweenness relation \({\cal B}_s(P)={\cal B}_s(G)\).
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Rautenbach, D., Schäfer, P.M. Strict Betweennesses Induced by Posets as well as by Graphs. Order 28, 89–97 (2011). https://doi.org/10.1007/s11083-010-9154-4
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DOI: https://doi.org/10.1007/s11083-010-9154-4