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 -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