Discussiones Mathematicae Graph Theory 27(3) (2007) 507-526
doi: 10.7151/dmgt.1376

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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.

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Received 27 July 2006
Revised 2 March 2007
Accepted 2 March 2007