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arXiv · 2303.01689

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

Imed Zaguia
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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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Imed Zaguia. 2023-03-03. The Aharoni--Korman conjecture for posets whose incomparability graph is locally finite. https://arxiv.org/abs/2303.01689

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