Constructing the Spectrum for Maximum Packings of Complete Graphs with Stars of Size Six
Graduation Year
2023
Publication Date
Spring 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
COinS
Comments
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