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- A chord of a graph cycle is an edge not in the edge set of whose endpoints lie in the vertex set (West 2000, p. 225). For example, in the diamond graph as labeled above, the edge is a chord of the cycle. The motivation for the term "chord" is geometric.
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In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with a finite system of chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other.
5 days ago · A chord of a graph cycle is an edge not in the edge set of whose endpoints lie in the vertex set (West 2000, p. 225). For example, in the diamond graph as labeled above, the edge is a chord of the cycle . The motivation for the term "chord" is geometric.
A circle graph is the intersection graph of chords on a circle. They are closed under local complementation. Every circle graph is a vertex-minor of a comparability grid. chord diagram circle graph G v
Sep 22, 2024 · Graphclass: circle. A graph is a circle graph if it is the intersection graph of chords in a circle. Let the local complement G*v result from G by complementing G [N (v)]. Two graphs are said to be locally equivalent if one results from the other by a series of local complements.
Can we describe the structure of graphs G without a vertex-minor isomorphic to H? If G is a circle graph, this is captured by immersions of its tour graph. (Robertson and Seymour; DeVos, McDonald, Mohar, Scheide, 13; Wollan, 15) What if H is a circle graph? Then G can be \recursively decomposed" along \simple" vertex partitions.
A graph G is chordal if it is the intersection graph of subtrees of a tree T. In particular T can be chosen such that each node of T corresponds to a maximal clique of G and the subtrees T v consist of precisely those maximal cliques in G that contain v. T is then called the clique tree of G.
In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle. Equivalently, every induced cycle in the graph should have exactly three vertices.
