The number of edges in a subgraph of a Hamming graph

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Abstract

Let G be a subgraph of the Cartesian product Hamming graph (Kp)r with n vertices. Then the number of edges of G is at most (12)(p − 1) logp n, with equality holding if and only G is isomorphic to (Kp)s for some sr.

Keywords

Average size
Maximum size
Completely decomposable

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