An antichain A of a well-founded quasi-order Q is canonical if for every ideal F of Q, F has an infinite antichain if and only if F ∩ A is infinite. In this paper we characterize the obstructions to having a canonical antichain. As an application we show that, under the induced subgraph relation, the class of finite graphs does not have a canonical antichain. In contrast, this class does have a canonical antichain with respect to the subgraph relation. © 2008 Elsevier B.V. All rights reserved.
Publication Source (Journal or Book title)
Ding, G. (2009). On canonical antichains. Discrete Mathematics, 309 (5), 1123-1134. https://doi.org/10.1016/j.disc.2007.12.018