TR-177: Representing Partial Orders by Polygons and Circles in the Plane

Abstract

The representation of partial orders as containment orders for sets of geometric objects has attracted much attention over the last few years. New results for the cases of polygon ( n-gon) and circle orders are presented:

( i) A result which relates the crossing number of a poset to the intersection number of polygon orders is given;
(ii) Two promising schemes for constructing circle orders for three-dimensional posets are shown not to work;
(iii) The Hiraguchi partial order is shown to be a circle order with circles of only two radii;
(iv) The question of which bipartite partial orders are circle orders is examined.