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arXiv · 1811.07959

The Aharoni--Korman conjecture for $N$-free posets with no infinite antichain

Imed Zaguia
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Abstract

We give a necessary and sufficient condition for a $P_4$-free graph to be a cograph. This allows us to obtain a simple proof of the fact that finite $P_4$-free graphs are finite cographs. We also prove that $N$-free chain complete posets and $N$-free posets with no infinite antichains are series-parallel. As a consequence, we obtain that every $N$-free poset with no infinite antichain has a chain and a partition into antichains so that each part intersects the chain. This answers a conjecture of Aharoni and Korman (Order \textbf{9} (1992) 245--253) in this case.

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Imed Zaguia. 2018-11-19. The Aharoni--Korman conjecture for $N$-free posets with no infinite antichain. https://arxiv.org/abs/1811.07959

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