On multipartite posets

2007/06/11 by Geir Agnarsson, Agnarsson, Geir
Mathematics · #06A07 #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO #msc:06A07

paper · pdf · doi:10.48550/arxiv.0706.1529

6 pages

arxiv created 2007/06/11 · openalex publication_date 2007/06/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A poset P = (X,\preceq) is \em m-partite if X has a partition X = X₁ ∪ ... ∪ X_m such that (1) each X_i forms an antichain in P, and (2) x\prec y implies x∈ X_i and y∈ X_j where i<j. In this article we derive a tight asymptotic upper bound on the order dimension of m-partite posets in terms of m and their bipartite sub-posets in a constructive and elementary way.

Related

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• Antichain Simplices
• A note on blockers in posets
• Poset Ramsey Number R(P, Qn). I. Complete Multipartite Posets
• A generalization of a theorem of Erné