Efficient Extraction of Multiple Kuratowski Subdivisions [chapter]

Markus Chimani, Petra Mutzel, Jens M. Schmidt
Graph Drawing  
A graph is planar if and only if it does not contain a Kuratowski subdivision. Hence such a subdivision can be used as a witness for non-planarity. Modern planarity testing algorithms allow to extract a single such witness in linear time. We present the first linear time algorithm which is able to extract multiple Kuratowski subdivisions at once. This is of particular interest for, e.g., Branch-and-Cut algorithms which require multiple such subdivisions to generate cut constraints. The
more » ... aints. The algorithm is not only described theoretically, but we also present an experimental study of its implementation.
doi:10.1007/978-3-540-77537-9_17 dblp:conf/gd/ChimaniMS07 fatcat:rgxcokmuvbehribc3nfek34ofm