Sequentially Perfect and Uniform One-Factorizations of the Complete Graph
Date
2005
Authors
Dinitz, Jeffrey H.
Dukes, Peter J.
Stinson, Douglas R.
Journal Title
Journal ISSN
Volume Title
Publisher
The Electronic Journal of Combinatorics
Abstract
In 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).
Description
Keywords
Citation
Dinitz, 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/10.37236/1898