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2007•Discussiones Mathematicae Graph TheoryOpen access

The structure and existence of 2-factors in iterated line graphs

Michael J. Ferrara, Ronald J. Gould, Stephen G. Hartke

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Abstract

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.

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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.

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Available abstract

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.

Key concepts: Combinatorics, Mathematics, Iterated function, Line graph, Discrete mathematics, Hamiltonian path, Graph, Pancyclic graph

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