#### Title

Constructing the Spectrum for Maximum Packings of Complete Graphs with Stars of Size Six

#### Graduation Year

2023

#### Abstract

A 6-star is the complete bipartite graph $K_{1,6}$. A \emph{packing of $K_{n}$ with 6-stars} is a set of edge disjoint subgraphs of $K_{n}$, each of which is isomorphic to $S_{6}$. The set of edges of $K_{n}$ which are not used in the packing is called the leave and is denoted by $L$. The packing is called \emph{maximum} if $|L|$ is minimum with respect to all such packings. We show that every possible leave graph is achievable as the leave of a maximum packing of $K_{n}$ with 6-stars.

#### Disciplines

Mathematics

#### Recommended Citation

Nie, Zihan, "Constructing the Spectrum for Maximum Packings of Complete Graphs with Stars of Size Six" (2023). *Honors Projects*. 28.

https://digitalcommons.iwu.edu/math_honproj/28

## Comments

At the request of the author, this paper is not available for download. Bona fide researchers may consult it by visiting the University Archives in Tate Archives & Special Collections; contact archives@iwu.edu for details.