Nonplanarity of Iterated Line Graphs

الملخص EN

The 1-crossing index of a graph G is the smallest integer k such that the kth iterated line graph of G has crossing number greater than 1.

In this paper, we show that the 1-crossing index of a graph is either infinite or it is at most 5.

Moreover, we give a full characterization of all graphs with respect to their 1-crossing index.