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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 15 possible chord diagrams on six cyclically ordered points. In mathematics, a chord diagram consists of a cyclic order on a set of objects, together with a one-to-one pairing (perfect matching) of those objects.
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.
In the 2nd century AD, Ptolemy compiled a more extensive table of chords in his book on astronomy, giving the value of the chord for angles ranging from 1 / 2 to 180 degrees by increments of 1 / 2 degree. Ptolemy used a circle of diameter 120, and gave chord lengths accurate to two sexagesimal (base sixty) digits after the ...
book 1. A book, book graph, or triangular book is a complete tripartite graph K 1,1,n; a collection of n triangles joined at a shared edge. 2. Another type of graph, also called a book, or a quadrilateral book, is a collection of 4-cycles joined at a shared edge; the Cartesian product of a star with an edge. 3.
Another result found by Elias Dahlhaus is: A bipartite graph B = (X,Y,E) is chordal bipartite if and only if the split graph resulting from making X a clique is strongly chordal. [4] A bipartite graph B = (X,Y,E) is chordal bipartite if and only if every induced subgraph of B has a maximum X-neighborhood ordering and a maximum Y-neighborhood ...
Every perfectly orderable graph is a perfect graph. [1] Chordal graphs are perfectly orderable; a perfect ordering of a chordal graph may be found by reversing a perfect elimination ordering for the graph. Thus, applying greedy coloring to a perfect ordering provides an efficient algorithm for optimally coloring chordal graphs.
It is possible to determine whether a graph is strongly chordal in polynomial time, by repeatedly searching for and removing a simple vertex.If this process eliminates all vertices in the graph, the graph must be strongly chordal; otherwise, if this process finds a subgraph without any more simple vertices, the original graph cannot be strongly chordal.
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