.1 Four Problems
نویسنده
چکیده
We may then ask: Can we place bounds on g(m)? Can we characterize those subsets S which achieve the value of g(m)? Whereas in the case of vertex boundary, the optimal subsets S were found to be (near) Hamming balls, we shall see that for the edge isoperimetric problem these optimal sets are (near) subcubes. Because the problem of finding a set S with minimum edge boundary is dual to the problem of maximizing the number of edges between vertices in S, this result makes intuitive sense.
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