Pancomponented 2-factorizations of complete graphs

Dalibor Froncek; Brett Stevens

doi:10.1016/j.disc.2004.09.014

Pancomponented 2-factorizations of complete graphs

Dalibor Froncek, Brett Stevens

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

We pose and solve the existence of 2-factorizations of complete graphs and complete bipartite graphs that have the number of cycles per 2-factor varying, called pancomponented. Such 2-factorizations exist for all such graphs. The pancomponented problem requires a slight generalization of the methods used to solve pancyclic 2-factorization problem, by building 2-factors from cyclically generated 1-factors. These two solutions are offered as the basic approaches to constructing the two essential parameters of a 2-factorization: the size and the number of cycles in the 2-factors.

Original language	English (US)
Pages (from-to)	99-112
Number of pages	14
Journal	Discrete Mathematics
Volume	299
Issue number	1-3
DOIs	https://doi.org/10.1016/j.disc.2004.09.014
State	Published - Aug 28 2005

Bibliographical note

Funding Information:
Dalibor Froncek would like to thank the Department of Mathematics and Statistics of the University of Vermont where he was visiting while the early versions of this paper were written. Later versions were in part supported by the University of Minnesota Duluth Grant 177-1009. Brett Stevens would like to acknowledge the support of PIMS, MITACS, Simon Fraser University and an NSERC Grant.

Keywords

2-Factorization
Cycle decomposition
Oberwolfach problem

Publisher link

10.1016/j.disc.2004.09.014

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abstract = "We pose and solve the existence of 2-factorizations of complete graphs and complete bipartite graphs that have the number of cycles per 2-factor varying, called pancomponented. Such 2-factorizations exist for all such graphs. The pancomponented problem requires a slight generalization of the methods used to solve pancyclic 2-factorization problem, by building 2-factors from cyclically generated 1-factors. These two solutions are offered as the basic approaches to constructing the two essential parameters of a 2-factorization: the size and the number of cycles in the 2-factors.",

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N2 - We pose and solve the existence of 2-factorizations of complete graphs and complete bipartite graphs that have the number of cycles per 2-factor varying, called pancomponented. Such 2-factorizations exist for all such graphs. The pancomponented problem requires a slight generalization of the methods used to solve pancyclic 2-factorization problem, by building 2-factors from cyclically generated 1-factors. These two solutions are offered as the basic approaches to constructing the two essential parameters of a 2-factorization: the size and the number of cycles in the 2-factors.

AB - We pose and solve the existence of 2-factorizations of complete graphs and complete bipartite graphs that have the number of cycles per 2-factor varying, called pancomponented. Such 2-factorizations exist for all such graphs. The pancomponented problem requires a slight generalization of the methods used to solve pancyclic 2-factorization problem, by building 2-factors from cyclically generated 1-factors. These two solutions are offered as the basic approaches to constructing the two essential parameters of a 2-factorization: the size and the number of cycles in the 2-factors.

KW - 2-Factorization

KW - Cycle decomposition

KW - Oberwolfach problem

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Pancomponented 2-factorizations of complete graphs

Abstract

Bibliographical note

Keywords

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