Maximum degree growth of the iterated line graph.
A note on divisibility of the number of matchings of a family of graphs.
The structure and existence of 2-factors in iterated line graphs
We prove several results about the structure of 2-factors in iterated line graphs. Specifically, we give degree conditions on G that ensure L²(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 L²(G) with all cycle lengths specified. We also give a characterization of the graphs G where contains a 2-factor.
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