Minimum average distance subsets in the hamming cube
Discrete Mathematics
On the variance of average distance of subsets in the Hamming space
Discrete Applied Mathematics
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The edges of the complete graph on n vertices can be covered by ⌈lg n⌉ spanning complete bipartite subgraphs. However, the sum of the number of edges in these subgraphs is roughly (n2-4)lg n, while a cover consisting of n - 1 spanning stars uses only (n - 1)2 edges. We will show that the covering by spanning stars has the smallest total number of edges among all coverings of the clique by spanning complete bipartite subgraphs, except when n is 4 or 8. © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 223–227, 1998