Intersection graphs of Jordan arcs [chapter]

P. Ossona de Mendez, H. de Fraysseix
1999 Contemporary Trends in Discrete Mathematics  
A family of Jordan arcs, such that two arcs are nowhere tangent, defines a hypergraph whose vertices are the arcs and whose edges are the intersection points. We shall say that the hypergraph has a strong intersection representation and, if each intersection point is interior to at most one arc, we shall say that the hypergraph has a strong contact representation. We first characterize those hypergraphs which have a strong contact representation and deduce some sufficient conditions for a
more » ... ditions for a simple planar graph to have a strong intersection representation. Then, using the Four Color Theorem, we prove that a large class of simple planar graphs have a strong intersection representation.
doi:10.1090/dimacs/049/02 dblp:conf/dimacs/MendezF97 fatcat:j2rm56eb7rf4bi3bxeow7zxc3q