the algorithms of and are based on characterizations of line graphs involving odd triangles (triangles in the line graph with the property that there exists another vertex adjacent to an odd number of triangle vertices). however, the algorithm of uses only whitney's isomorphism theorem. it is complicated by the need to recognize deletions that cause the remaining graph to become a line graph, but when specialized to the static recognition problem only insertions need to be performed, and the algorithm performs the following steps: