(while the total graph of a hypergraph is still a hypergraph). We notice that, in the case of graphs, the incidence graph is the complete subdivision  ( http://en.wikipedia.org/wiki/Graph_subdivision#Subdivisions ) of G. Guedes&Markenzon(2005)  ( http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382005000300005 ) cite Johnson&Pollak(1987)  ( http://www3.interscience.wiley.com/journal/113388370/abstract ) as having used a similar structure for studying Zykov planarity of