Outerplanarity of line graphs and iterated line graphs

Huiqiu Lin, Weihua Yang, Hailiang Zhang, Jinlong Shu
2011 Applied Mathematics Letters  
The outerplanar index of a graph G is the smallest integer k such that the kth iterated line graph of G is non-outerplanar. In this note, we show: (i) the characterization of the forbidden subgraphs for graphs with outerplanar line graphs; (ii) that the outerplanar index of a graph is either infinite or at most 3. Furthermore, we give a full characterization of all graphs with respect to their outerplanar index. Crown
doi:10.1016/j.aml.2011.02.011 fatcat:hrjke2llinauzd4yont22ddhtq