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A graph is chordal if and only if it has a perfect elimination ordering. [3] Rose, Lueker & Tarjan (1976) (see also Habib et al. 2000) show that a perfect elimination ordering of a chordal graph may be found efficiently using an algorithm known as lexicographic breadth-first search. This algorithm maintains a partition of the vertices of the ...
The crossing pattern of chords in a chord diagram may be described by a circle graph, the intersection graph of the chords: it has a vertex for each chord and an edge for each two chords that cross. [3]
A chord (from the Latin chorda, meaning "bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a secant line. The perpendicular line passing through the chord's midpoint is called sagitta (Latin for "arrow").
Chord diagrams get their name from terminology used in geometry. A chord of a circle is a geometric line segment whose endpoints both lie on the circle. Chord diagrams are also known as radial network diagrams and may sometimes be referred to as a type of circular layout.
In graph theory, a branch of mathematics, a chordal completion of a given undirected graph G is a chordal graph, on the same vertex set, that has G as a subgraph. A minimal chordal completion is a chordal completion such that any graph formed by removing an edge would no longer be a chordal completion.
A chordal bipartite graph is not chordal (unless it is a forest); it is a bipartite graph in which every cycle of six or more vertices has a chord, so the only induced cycles are 4-cycles. 5. A chord of a circle is a line segment connecting two points on the circle; the intersection graph of a collection of chords is called a circle graph .
In geometry, a circular segment or disk segment (symbol: ⌓) is a region of a disk [1] which is "cut off" from the rest of the disk by a straight line. The complete line is known as a secant, and the section inside the disk as a chord. [2]
Bipartite graph, a graph without odd cycles (cycles with an odd number of vertices) Cactus graph, a graph in which every nontrivial biconnected component is a cycle; Cycle graph, a graph that consists of a single cycle; Chordal graph, a graph in which every induced cycle is a triangle; Directed acyclic graph, a directed graph with no directed ...