The Aharoni--Korman conjecture for posets whose incomparability graph is locally finite

2023/03/03 by Imed Zaguia, Zaguia, Imed
Computer Science · Mathematics · #06A6 #06F15 #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Functional Equations Stability Results

paper · pdf · doi:10.48550/arxiv.2303.01689

openalex publication_date 2023/03/03 · openalex created_date 2023/03/07 · openalex updated_date 2026/07/28

Abstract

Aharoni and Korman (Order 9 (1992) 245--253) have conjectured that every ordered set without infinite antichains possesses a chain and a partition into antichains so that each part intersects the chain. The conjecture is verified for posets whose incomparability graph is locally finite. It follows that the conjecture is true for (3 + 1)-free posets with no infinite antichains.

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