Uniformly resolvable decompositions of Kv in 1-factors and 4-stars

Authors

Melissa S. Keranen, Michigan Technological UniversityFollow
Donald L. Kreher, Michigan Technological UniversityFollow
Salvatore Milici, Universit`a di Catania
Antoinette Tripodi, Universit`a di Messina

Document Type

Article

Publication Date

2020

Department

Department of Mathematical Sciences

Abstract

If X is a connected graph, then an X-factor of a larger graph is a spanning subgraph in which all of its components are isomorphic to X. A uniformly resolvable {X, Y }-decomposition of the complete graph K_v is an edge decomposition of K_v into exactly r X-factors and s Y -factors. In this article we determine necessary and sufficient conditions for when the complete graph K_v has a uniformly resolvable decompositions into 1-factors and K_1,4-factors.

Publisher's Statement

© The author(s). Released under the CC BY 4.0 International License. Publisher’s version of record: https://ajc.maths.uq.edu.au/pdf/76/ajc_v76_p055.pdf

Publication Title

AUSTRALASIAN JOURNAL OF COMBINATORICS

Recommended Citation

Keranen, M. S., Kreher, D. L., Milici, S., & Tripodi, A. (2020). Uniformly resolvable decompositions of Kv in 1-factors and 4-stars. AUSTRALASIAN JOURNAL OF COMBINATORICS, 76(1), 55-72.
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/1527

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Version

Publisher's PDF