In this paper we introduce a new technique to analyze families of rankings focused on the study of structural properties of a new type of graphs. Given a finite number of elements and a family of rankings of those elements, we say that two elements compete when they exchange their relative positions in at least two rankings. This allows us to define an undirected graph by connecting elements th...

Kelly showed that there exist planar posets of arbitrarily large dimension, and Streib and Trotter showed that the dimension of a poset with a planar cover graph is bounded in terms of its height. Here we continue the study of conditions that bound the dimension of posets with planar cover graphs. We show that if P is a poset with a planar comparability graph, then the dimension of P is at most...

A P4-transversal of a graph G is a set of vertices T which meets every P4 of G. A P4transversal T is called stable if there are no edges in the subgraph of G induced by T . It has been previously shown by Hoàng and Le that it is NP -complete to decide whether a comparability (and hence perfect) graph G has a stable P4-transversal. In the following we show that the problem is NP -complete for ch...

Birkhoff’s fundamental theorem on distributive lattices states that for every distributive lattice L there is a poset PL whose lattice of down-sets is order-isomorphic to L. Let G(L) denote the cover graph of L. In this paper, we consider the following problems: Suppose we are simply given PL. How do we compute the eccentricity of an element of L in G(L)? How about a center and the radius of G(...

The independent set on a graph G = (V, E) is a subset of V such that no two vertices in the subset have an edge between them. The maximum independent set problem on G seeks to identify an independent set with maximum cardinality, i.e. maximum independent set or MIS. The maximum independent set problem on a general graph is known to be NP-complete. On certain classes of graphs MIS can be compute...

A pair of linear orders L, L′ on an n-element set V is a concordance pair if the Kendall and Spearman correlation measures between L and L′ coincide. A graph is called concordance graph if it has the same number of induced three-vertex one-edged subgraphs as induced three-vertex twoedged subgraphs. It is known (see Fishburn and Monjardet (2000)) that (L, L′) is a concordance pair if and only if...

The development of a recently proposed method for calculating molecular properties is outlined. The approach is based on the idea of constructing optimized compound samples for structure-property or structure-activity correlations by means of the so-cailed comparability graphs (CG) of isomeric compounds. A dynamic comparability principle is devised, proceeding from a series of standard molecula...

Falcon-AO is an automatic tool for aligning ontologies. There are two matchers integrated in Falcon-AO: one is a matcher based on linguistic matching for ontologies, called LMO; the other is a matcher based on graph matching for ontologies, called GMO. In Falcon-AO, GMO takes the alignments generated by LMO as external input and outputs additional alignments. Reliable alignments are gained thro...

In this paper, we prove necessary conditions for Hibi rings to satisfy Green–Lazarsfeld property [Formula: see text] and text]. We also show that if a ring satisfies text], then it is polynomial or has linear resolution. Therefore, all as well. As consequence, characterize distributive lattices whose comparability graph chordal in terms of the subposet join-irreducibles lattice. Moreover, compl...

This paper studies market competition when firms can influence consumers’ ability to compare market alternatives, through their choice of price “formats”. We introduce random graphs as a tool for modeling limited comparability of formats. Our main results concern the interaction between firms’ equilibrium price and format decisions and its implications for industry profits and consumer switchin...