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On the left a set of polygons inscribed in a circle; on the right the relative Polygon-circle graph (intersection graph of the polygon). At the bottom the alternating sequence of polygons around the circle.
(graph theory) A graph(set of connected points) in which each vertex corresponds to a convex polygon circumscribed in a common circle, and in which (graph) vertices are adjacent iff their corresponding polygons intersect geometrically.
2004, Jan Kratochvíl, Martin Pergel, “Two Results on Intersection Graphs of Polygons”, in Giuseppe Liotta, editor, GD 2003 International Symposium on Graph Drawing (Lecture Notes in Computer Science), volume 2912, Springer-Verlag, →DOI, →ISBN, page 60:
A common generalization of these two are polygon-circle graphs, intersection graphs of convex polygons inscribed to the circle. This class was first suggested by M. Fellows in 1988, when it was pointed out that this class of graphs is closed under taking induced minors.
