The intersection graph
of a generic surface
is the set of values which are either singularities or intersections.
It is a multigraph whose edges are transverse intersections of two
surfaces and whose vertices are triple intersections and branch values.
has
an enhanced graph structure which Gui-Song Li referred to as a “daisy graph”. If
is oriented, then the orientation further refines the structure of
into
what Li called an “arrowed daisy graph”.
Li left open the question “which arrowed daisy graphs can be realized as the
intersection graph of an oriented generic surface?” The main theorem of this article
will answer this. I will also provide some generalizations and extensions to this
theorem in Sections 4 and 5.
Keywords
generic surfaces, immersed surfaces in 3-manifolds,
intersection graph
