English

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

Combinatorics 2023-03-06 v1

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)(3 + 1)-free posets with no infinite antichains.

Keywords

Cite

@article{arxiv.2303.01689,
  title  = {The Aharoni--Korman conjecture for posets whose incomparability graph is locally finite},
  author = {Imed Zaguia},
  journal= {arXiv preprint arXiv:2303.01689},
  year   = {2023}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1811.07959

R2 v1 2026-06-28T08:58:40.955Z