Circle graph equation

Intersection graph of a chord diagram

For the chart, see Pie chart.

For other diagrams, see Circle diagram, Smith chart, and Nyquist plot.

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.

Algorithmic complexity

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After earlier polynomial time algorithms,^[1]Gioan et al.

(2013) presented an algorithm for recognizing circle graphs in near-linear time.

When would you use a circle graph instead of a bar graph

Their method is slower than linear by a factor of the inverse Ackermann function, and is based on lexicographic breadth-first search. The running time comes from a method for maintaining the split decomposition of a graph incrementally, as vertices are added, used as a subroutine in the algorithm.

A number of other problems that are NP-complete on general graphs have polynomial time algorithms when restricted to circle graphs.

For instance, Kloks (1996) showed that

when is it appropriate to use a circle graph

circle graphs