The structure and existence of 2-factors in iterated line graphs
Michael J. Ferrara, Ronald J. Gould, Stephen G. Hartke · Discussiones Mathematicae Graph Theory · 2007
We prove several results about the structure of 2-factors in iterated line graphs.Specifically, we give degree conditions on G that ensure L 2 (G) contains a 2-factor with every possible number of cycles, and we give a sufficient condition for the existence of a 2-factor in L 2 (G) with all cycle lengths specified.We also give a characterization of the graphs G where L k (G) contains a 2-factor.