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comparability graph

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  • Comparability graph — In graph theory, a comparability graph is an undirected graph that connects pairs of elements that are comparable to each other in a partial order. Comparability graphs have also been called transitively orientable graphs, partially orderable… …   Wikipedia

  • Comparability — See also: Comparison In mathematics, any two elements x and y of a set P that is partially ordered by a binary relation ≤ are comparable when either x ≤ y or y ≤ x. If it is not the case that x and y are comparable, then they are called… …   Wikipedia

  • Quasi-threshold graph — In graph theoretic mathematics, a quasi threshold graph is a graph that can be constructed using the following rules: # K 1 is a quasi threshold graph #If G is a quasi threshold graph, then so is the graph obtained by adding a new vertex… …   Wikipedia

  • Interval graph — In graph theory, an interval graph is the intersection graph of a set of intervals on the real line. It has one vertex for each interval in the set, and an edge between every pair of vertices corresponding to intervals that intersect.Formally,… …   Wikipedia

  • Neighbourhood (graph theory) — A graph consisting of 6 vertices and 7 edges For other meanings of neighbourhoods in mathematics, see Neighbourhood (mathematics). For non mathematical neighbourhoods, see Neighbourhood (disambiguation). In graph theory, an adjacent vertex of a… …   Wikipedia

  • Split graph — In graph theory, a split graph is a graph in which the vertices can be partitioned into a clique and an independent set. Split graphs were first studied by Földes and Hammer in two papers in 1977, and independently introduced by Tyshkevich and… …   Wikipedia

  • Distance-hereditary graph — A distance hereditary graph. In graph theoretic mathematics, a distance hereditary graph (also called a completely separable graph)[1] is a graph in which the distances in any connected induced subgraph are the same as they are in the original… …   Wikipedia

  • Perfect graph — The Paley graph of order 9, colored with three colors and showing a clique of three vertices. In this graph and each of its induced subgraphs the chromatic number equals the clique number, so it is a perfect graph. In graph theory, a perfect… …   Wikipedia

  • Dilworth's theorem — In mathematics, in the areas of order theory and combinatorics, Dilworth s theorem characterizes the width of any finite partially ordered set in terms of a partition of the order into a minimum number of chains. It is named for the mathematician …   Wikipedia

  • Modular decomposition — In graph theory, the modular decomposition is a decomposition of an undirected graph into subsets of vertices called modules. A module is a generalization of a connected component of a graph. Unlike connected components, however, one module can… …   Wikipedia

  • Order dimension — A partial order of dimension 4 (shown as a Hasse diagram) and four total orderings that form a realizer for this partial order. In mathematics, the dimension of a partially ordered set (poset) is the smallest number of total orders the… …   Wikipedia

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