| Maximum $2\times 3$ Grid-Block Packings of $K_v$ |
| Received:December 31, 2012 Revised:July 07, 2013 |
| Key Words:
packing complete graph Cartesian product.
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| Abstract: |
| Let $K_v$ be the complete graph on $v$ vertices, and $G$ a finite simple undirected graph without isolated vertices. A $G$-packing of $K_v$, denoted by $(v,G,1)$-packing, is a pair $(X,\mathcal{A})$ where $X$ is the vertex set of $K_v$ and $\mathcal{A}$ is a family of edge-disjoint subgraphs isomorphic to $G$ in $K_v$. In this paper, the maximum number of subgraphs in a $(v,G,1)$-packing is determined when $G$ is $K_2\times K_3$, the Cartesian product of $K_2$ and $K_3$, leaving two orders undetermined. This design originated from the use of DNA library screening. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2014.02.002 |
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