DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

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Discussiones Mathematicae Graph Theory

THE STRUCTURE AND EXISTENCE OF 2-FACTORS IN ITERATED LINE GRAPHS

 Michael Ferrara Department of Theoretical and Applied Mathematics The University of Akron Akron, OH 44325, USA e-mail: mjf@uakron.edu Ronald J. Gould Department of Mathematics and Computer Science Emory University, Atlanta, GA 30322, USA e-mail: rg@mathcs.emory.edu Stephen G. Hartke Department of Mathematics University of Nebraska-Lincoln Lincoln, NE 68588-0130, USA e-mail: hartke@unl.edu

Abstract

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 Lk(G) contains a 2-factor.

Keywords: line graph, 2-factor, iterated line graph, cycle.

2000 Mathematics Subject Classification: 05C38, 05C70.

References

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