Intersection classes of graphs
Polygon-circle graph
In the mathematical discipline of graph theory, a polygon-circle graph is an intersection graph of a set of convex polygons all of whose vertices lie on a common circle. These graphs have also been called spider graphs. This class of graphs was first suggested by Michael Fellows in 1988, motivated by the fact that it is closed under edge contraction and induced subgraph operations. A polygon-circle graph can be represented as an "alternating sequence". Such a sequence can be gained by perturbing the polygons representing the graph (if necessary) so that no two share a vertex, and then listing for each vertex (in circular order, starting at an arbitrary point) the polygon attached to that vertex. (Wikipedia).
