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A geometric graph \G is a simple graph drawn in the plane, on points ingeneral position, with straight-line edges. We call \G a geometric realizationof the underlying abstract graph G. A geometric homomorphism from \G to \H is avertex map that preserves adjacencies and crossings (but not necessarilynon-adjacencies or non-crossings). Geometric homomorphisms can be used todefine a partial order on the set of isomorphism classes of geometricrealizations of an abstract graph G. In this paper, the homomorphism poset ofK_{3,3} is determined.

The Homomorphism Poset of $K_{3,3}$