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, Volume 28, Issue 1, pp 89–97 | Cite as

Strict Betweennesses Induced by Posets as well as by Graphs

  • Dieter RautenbachEmail author
  • Philipp Matthias Schäfer
Article

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 \({\cal B}_s(P)={\cal B}_s(G)\).

Keywords

Poset Graph Induced path Betweenness Convexity 

Mathematics Subject Classifications (2010)

05C99 06A06 52A01 52A37 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Institut für MathematikIlmenauGermany

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