Polygon-circle graph

<p>In the <a href="/facts/Mathematics/pxTouaz4">mathematical</a> discipline of <a href="/facts/Graph_theory/VVPCd4TX">graph theory</a>, a polygon-circle graph is an <a href="/facts/Intersection_graph/IehIvyR3">intersection graph</a> of a set of <a href="/facts/Convex_polygon/7x35w610">convex polygons</a> all of whose <a href="/facts/Vertex_(geometry)/ID3cea9z">vertices</a> lie on a common circle. These graphs have also been called spider graphs. This class of graphs was first suggested by <a href="/facts/Michael_Fellows/Mmlrxg5L">Michael Fellows</a> in 1988, motivated by the fact that it is closed under <a href="/facts/Edge_contraction/PRqKXEkj">edge contraction</a> and <a href="/facts/Induced_subgraph/G3EUC0MQ">induced subgraph</a> operations.
</p><p>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.
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Polygon-circle graph open-in-new

Polygon-circle graph