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A circle graph is the intersection graph of a family of chords of a circle. A given graph is a circle graph if and only if each of the quotients of its split decomposition is a circle graph, so testing whether a graph is a circle graph can be reduced to the same problem on the prime quotient graphs of the graph.
If a graph is both a split graph and an interval graph, then its complement is both a split graph and a comparability graph, and vice versa. The split comparability graphs, and therefore also the split interval graphs, can be characterized in terms of a set of three forbidden induced subgraphs. [7] The split cographs are exactly the threshold ...
When modelling relations between two different classes of objects, bipartite graphs very often arise naturally. For instance, a graph of football players and clubs, with an edge between a player and a club if the player has played for that club, is a natural example of an affiliation network, a type of bipartite graph used in social network analysis.
If a chart plots 10 colors or fewer, then by default it uses every other one: The colors can be manually set in a graph by adding them to the 'colors' parameter. For example, for two pie charts, the first of which is default and the second of which omits some colors in the first, you would manually enter your selections from the default 20:
Wheel graphs W 2n+1, for n ≥ 2, are not word-representable and W 5 is the minimum (by the number of vertices) non-word-representable graph. Taking any non-comparability graph and adding an apex (a vertex connected to any other vertex), we obtain a non-word-representable graph, which then can produce infinitely many non-word-representable ...
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A graphical game is represented by a graph , in which each player is represented by a node, and there is an edge between two nodes and iff their utility functions are dependent on the strategy which the other player will choose.
The NFL has declared that any players kneeling during the national anthem will now be hit with a fine. Looking at the racial breakdown of the league helps understand why. It’s striking how much ...
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