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In any graph, a vertex separator is a set of vertices the removal of which leaves the remaining graph disconnected; a separator is minimal if it has no proper subset that is also a separator. According to a theorem of Dirac (1961) , chordal graphs are graphs in which each minimal separator is a clique; Dirac used this characterization to prove ...
A chord chart. Play ⓘ. A chord chart (or chart) is a form of musical notation that describes the basic harmonic and rhythmic information for a song or tune. It is the most common form of notation used by professional session musicians playing jazz or popular music.
Chord diagrams are conventionally visualized by arranging the objects in their order around a circle, and drawing the pairs of the matching as chords of the circle. The number of different chord diagrams that may be given for a set of 2 n {\displaystyle 2n} cyclically ordered objects is the double factorial ( 2 n − 1 ) ! ! {\displaystyle (2n ...
Screenshot from "A Thousand Fibers Connect Us — Wikipedia's Global Reach", winning entry of the WikiViz 2011 Data Visualization Challenge. Lines represent readership of different Wikipedia language versions (lower half) from countries (top half) A chord diagram is a graphical method of displaying the inter-relationships between data in a ...
A chord diagram may refer to: Chord diagram (music) , a diagram showing the fingering of a chord on a guitar or other fretted musical instrument Chord diagram (information visualization) , a diagram showing a many-to-many relationship between objects as curved arcs within a circle
The graph G (excluding red edges) is a subgraph of the chordal graph H (including red edges) which shares the same vertex set, making H a chordal completion of G. Removing any of the newly added red edges causes the graph to no longer be chordal, making it a minimal chordal completion.
Equal chords are subtended by equal angles from the center of the circle. A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle. If the line extensions (secant lines) of chords AB and CD intersect at a point P, then their lengths satisfy AP·PB = CP·PD (power of a point theorem).
In the first graph, the 8-cycle has odd edges 3-6 and 2-7, and the 6-cycles each also have one of those two edges as an odd edge. In the second graph, the two red edges need to be added, one so that the 8-cycle has an odd edge, and the other to make an odd chord for the 6-cycle formed by the newly inserted edge.