In graph theory and order theory, a comparability graph is an undirected graph that connects pairs of elements that are comparable to each other in a...

graph. Finite comparability graphs (and their complementary incomparability graphs) are always perfect. A clique, in a comparability graph, comes from a...

any two comparable elements. Thus, a clique in a comparability graph corresponds to a chain, and an independent set in a comparability graph corresponds...

complement is a comparability graph, it follows that graph and its complement are both interval graphs if and only if the graph is both a split graph and a permutation...

graph in F is also locally F. For instance, every chordal graph is locally chordal; every perfect graph is locally perfect; every comparability graph...

2003), comparability graph with maximum degree 4 (Ochem 2017), line graph of a bipartite graph with maximum degree 4 (Gonçalves & Ochem 2009), graph with...

special cases of the distance-hereditary graphs, permutation graphs, comparability graphs, and perfect graphs. Any cograph may be constructed using the...

that such a graph is perfect." Trivially perfect graphs are also known as comparability graphs of trees, arborescent comparability graphs, and quasi-threshold...

are comparable in the partial order. Equivalently, a comparability graph is a graph that has a transitive orientation. Many other classes of graphs can...

Look up comparability in Wiktionary, the free dictionary. In mathematics, two elements x and y of a set P are said to be comparable with respect to a...

relationship in directed trees and directed series–parallel graphs. The comparability graphs of series-parallel partial orders are cographs. Series-parallel...

graphs) and is useful to design efficient algorithms for the recognition of some graph classes, for finding transitive orientations of comparability graphs...

Perfect graphs include many important graphs classes including bipartite graphs, chordal graphs, and comparability graphs. The complement of a graph has an...

{\overline {G}}} are comparability graphs. A graph G {\displaystyle G} is a permutation graph if and only if it is the comparability graph of a partially ordered...

induced subgraphs of comparability graphs are themselves comparability graphs, so Mirsky's theorem states that comparability graphs are perfect. Analogously...

circular-arc graphs and of co-comparability graphs (i.e. of the complements of comparability graphs, which also contain permutation graphs), both having...

connected component of its comparability graph is graded, so further characterizations will suppose this comparability graph to be connected. On each connected...

set, a poset-based approach to quantum gravity Comparability graph – Graph linking pairs of comparable elements in a partial order Complete partial order –...

comparability graphs of the partial orders of dimension two are exactly the permutation graphs, graphs that are both themselves comparability graphs and...

Graph neural networks (GNN) are specialized artificial neural networks that are designed for tasks whose inputs are graphs. One prominent example is molecular...

representing a graph as a unit disk graph may require exponentially many bits for the coordinates of the disk centers. Low-dimensional comparability graphs The comparability...

maximal independent set in the comparability graph of Q, or a maximal clique in the complement of the comparability graph, so algorithms for the clique...

transfinite recursion). In 2004, the result was generalized from trees to graphs as the Robertson–Seymour theorem, a result that has also proved important...

The graph of a monotone operator G ( T ) {\displaystyle G(T)} is a monotone set. A monotone operator is said to be maximal monotone if its graph is a...

A graph database (GDB) is a database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data. A key...

graph; perfect graphs include many well-known graph classes including the bipartite graphs, chordal graphs, and comparability graphs. In his 1961 and...

finite. Comparable. Two elements x and y of a poset P are comparable if either x ≤ y or y ≤ x. Comparability graph. The comparability graph of a poset...

permutation graph, in turn they are a special case of the family of the complements of comparability graphs known as cocomparability graphs. A unit disk graph is...

In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to...

important in graph theory, since they generalise several important classes of graphs, e.g. circle graphs, 3-colorable graphs and comparability graphs. It was...