In this paper we consider languages of labelled N -free posets over countable and scattered linear orderings. We prove that a language of such posets is series-rational if and only if it is recognizable by a finite depth-nilpotent algebra if and only if it is bounded-width and monadic second-order definable. This extends previous results on languages of labelled N -free finite and ω-posets and ...

A long-standing conjecture states that posets with the normalized matching property are nested chain orders. We verify this conjecture for posets of rank 2.

Given a directed graph G = (V,E) and an integer k ≥ 1, a k-transitive-closure-spanner (k-TCspanner) of G is a directed graph H = (V,EH) that has (1) the same transitive-closure as G and (2) diameter at most k. In some applications, the shortcut paths added to the graph in order to obtain small diameter can use Steiner vertices, that is, vertices not in the original graph G. The resulting spanne...

The queue number of a poset is the its cover graph when vertex order linear extension poset. Heath and Pemmaraju conjectured that every width w has at most w. conjecture been confirmed for posets $$w=2$$ planar with 0 1. In contrast, refused by family general (non-planar) $$w>2$$ . this paper, we study layouts two-dimensional posets. First, construct $$w > 2$$ $$2(w - 1)$$ , thereby disproving ...

In order to be able use methods of universal algebra for investigating posets, we assigned every pseudocomplemented poset, relatively poset and sectionally a certain (based on commutative directoid or λ-lattice) which satisfies identities implications. We show that the algebras fully characterize given corresponding posets. A kind symmetry can seen in relationship between classes mentioned pose...

This work is devoted to give a charcaterization of a pomonoid $S$ such that all cyclic $S$-posets are regular injective.