Sequentially Perfect and Uniform One-Factorizations of the Complete Graph

Simple item page
dc.contributor.authorDinitz, Jeffrey H.
dc.contributor.authorDukes, Peter J.
dc.contributor.authorStinson, Douglas R.
dc.date.accessioned2021-03-01T23:52:30Z
dc.date.available2021-03-01T23:52:30Z
dc.date.copyright2005en_US
dc.date.issued2005
dc.description.abstractIn this paper, we consider a weakening of the de nitions of uniform and perfect one-factorizations of the complete graph. Basically, we want to order the 2n − 1 one-factors of a one-factorization of the complete graph K2n in such a way that the union of any two (cyclically) consecutive one-factors is always isomorphic to the same two-regular graph. This property is termed sequentially uniform; if this two-regular graph is a Hamiltonian cycle, then the property is termed sequentially perfect. We will discuss several methods for constructing sequentially uniform and sequentially perfect one-factorizations. In particular, we prove for any integer n 1 that there is a sequentially perfect one-factorization of K2n. As well, for any odd integer m > 1, we prove that there is a sequentially uniform one-factorization of K2tm of type (4; 4; : : : ; 4) for all integers t > 2 + dlog2me (where type (4; 4; : : : ; 4) denotes a two-regular graph consisting of disjoint cycles of length four).en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.identifier.citationDinitz, J. H., Dukes, P., & Stinson, D. R. (2005). Sequentially Perfect and Uniform One-Factorizations of the Complete Graph. The Electronic Journal of Combinatorics, 12. https://doi.org/10.37236/1898en_US
dc.identifier.urihttps://doi.org/10.37236/1898
dc.identifier.urihttp://hdl.handle.net/1828/12743
dc.language.isoenen_US
dc.publisherThe Electronic Journal of Combinatoricsen_US
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleSequentially Perfect and Uniform One-Factorizations of the Complete Graphen_US
dc.typeArticleen_US

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Dinitz_J_ElectronJComb_2005.pdf
Size:
397.24 KB
Format:
Adobe Portable Document Format
Description:
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
2 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

Faculty and Staff Publications
 
University of Victoria Libraries

We acknowledge and respect the Lək̓ʷəŋən (Songhees and Esquimalt) Peoples on whose territory the university stands, and the Lək̓ʷəŋən and W̱SÁNEĆ Peoples whose historical relationships with the land continue to this day.