Hypergraph Planarization

Abstract

A.A. Zykov was the first person to extend the notion of planarity to hyper-graphs [92]. According to [92] a hypergraph is called planar if it has a planar Konig representation. In general, such a definition of a planar hypergraph is not adequate for the planarity of an electrical circuit. In fact, in the layout of a planar circuit the nets correspond to trees which cannot be replaced by star-type subgraphs without creating nonplanarity in all cases. The limitation of using the Zykov hypergraph planarity definition to investigate circuit planarity was shown in [6, 22, 78]. These researches suggested different mathematical models for circuits and introduced corresponding definitions of circuit model planarity which are more suitable for solving the circuit planarization problem. The necessity of solving circuit planarization problems gave rise to a new definition of a planar hypergraph [83] based on the realization concept.