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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 ...
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 ...
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.
G is a claw-free AT-free graph if and only if all of its minimal chordal completions are proper interval graphs. And G is a cograph if and only if all of its minimal chordal completions are trivially perfect graphs. [1] A graph G has treewidth at most k if and only if G has at least one chordal completion whose maximum clique size is at most k + 1.
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 ...
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.
IV-V-I-vi chord progression in C major: 4: Major I–V–vi–IV: I–V–vi–IV chord progression in C: 4: Major I–IV– ♭ VII–IV: I–IV– ♭ VII–IV. 3: Mix. ii–V–I progression: ii–V–I: 3: Major ii–V–I with tritone substitution (♭ II7 instead of V7) ii– ♭ II –I: 3: Major ii-V-I with ♭ III + as dominant ...
[1] 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.