Splitting finite antichains in the homomorphism order
نویسنده
چکیده
A structural condition is given for finite maximal antichains in the homomorphism order of relational structures to have the splitting property. It turns out that non-splitting antichains appear only at the bottom of the order. Moreover, we examine looseness and finite antichain extension property for some subclasses of the homomorphism poset. Finally, we take a look at cut-points in this order.
منابع مشابه
On Finite Maximal Antichains in the Homomorphism Order
The relation of existence of a homomorphism on the class of all relational structures of a fixed type is reflexive and transitive; it is a quasiorder. There are standard ways to transform a quasiorder into a partial order – by identifying equivalent objects, or by choosing a particular representative for each equivalence class. The resulting partial order is identical in both cases. Properties ...
متن کاملAntichains in the homomorphism order of graphs
Denote by G and D, respectively, the the homomorphism poset of the finite undirected and directed graphs, respectively. A maximal antichain A in a poset P splits if A has a partition (B, C) such that for each p ∈ P either b ≤P p for some b ∈ B or p ≤p c for some c ∈ C. We construct both splitting and non-splitting infinite maximal antichains in G and in D. A point y ∈ P is a cut point in a pose...
متن کاملGeneralised Dualities and Finite Maximal Antichains
We fully characterise the situations where the existence of a homomorphism from a digraph G to at least one of a finite set H of directed graphs is determined by a finite number of forbidden subgraphs. We prove that these situations, called generalised dualities, are characterised by the non-existence of a homomorphism to G from a finite set of forests. Furthermore, we characterise all finite m...
متن کاملGeneralised dualities and maximal finite antichains in the homomorphism order of relational structures
The motivation for this paper is three-fold. First, we study the connectivity properties of the homomorphism order of directed graphs, and more generally for relational structures. As opposed to the homomorphism order of undirected graphs (which has no non-trivial finite maximal antichains), the order of directed graphs has finite maximal This research was partially supported by the EU Research...
متن کاملOn maximal finite antichains in the homomorphism order of directed graphs
We show that the pairs {T, DT } where T is a tree and DT its dual are the only maximal antichains of size 2 in the category of directed graphs endowed with its natural homomorphism ordering.
متن کامل