A graph is a circle graph if and only if it is the overlap graph of a set of intervals on a line.
12.
Every circle graph, as an intersection graph of line segments ( the chords of a circle ), is also a string graph.
13.
For recognizing distance-hereditary graphs and circle graphs, a further generalization of modular decomposition, called the split decomposition, is especially useful ( Spinrad, 2003 ).
14.
William Playfair invented several types of area and bar chart of economic data, and in 1801 the pie chart and circle graph, used to show part-whole relations.
15.
However, this also occasionally changes to include a more complex line graph, a circle graph, and on one occasion to-date, a graphic unrepresentative of an actual graph altogether.
16.
On the left a set of polygons inscribed in a circle; on the right the relative "'Polygon-circle graph "'( intersection graph of the polygons ).
17.
For instance, in a circle graph, the neighborhood of each vertex is a permutation graph, so a maximum clique in a circle graph can be found by applying the permutation graph algorithm to each neighborhood.
18.
For instance, in a circle graph, the neighborhood of each vertex is a permutation graph, so a maximum clique in a circle graph can be found by applying the permutation graph algorithm to each neighborhood.
19.
In particular, for circle graphs in which no sets of " k " or more chords all cross each other, it is possible to color the graph with as few as 21 \ cdot 2 ^ k-24k-24 colors.
20.
The problem of assigning edges to the two pages in a compatible way can be formulated as either an instance of 2-satisfiability, or as a problem of testing the bipartiteness of the circle graph whose vertices are the basepairs and whose edges describe crossings between basepairs.
