Simple graphs with this characteristic have a number of edges less than or equal to three times the number of vertices minus six.
This can be determined in linear time with the algorithm of Williamson or with that of Lempel, Even, and Cederbaum and it is logically equivalent to the existence of a topological K-5 or K-3,3 subgraph.  Simple graphs with this characteristic have a number of edges less than or equal to three times the number of vertices minus six. Duals are found only in graphs with this property, which is possessed by trees, cycles, and wheel graphs. FTP name the subject of a 1930 theorem by Kazimierz Kuratowski, the property of a graph that it can be rendered in two-space without having any edge cross?
This can be determined in linear time with the algorithm of Williamson or with that of Lempel, Even, and Cederbaum and it is logically equivalent to the existence of a topological K-5 or K-3,3 subgraph.  
planarity (accept word forms, e.g., that the graph is planar)