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In this paper, we extend two classical results about the density of subgraphs of hypercubes to subgraphs of Cartesian products of arbitrary connected graphs. Namely, we show that , where is the maximum ratio taken over all subgraphs of . We introduce the notions of VC‐dimension and VC‐density ...
In this article, we characterize the graphs G that are the retracts of Cartesian products of chordal graphs. We show that they are exactly the weakly modular graphs that do not contain K2, 3, the 4‐wheel minus one spoke , and the k‐wheels (for as induced subgraphs. We also show that these graphs G are exactly the cage‐amalgamation graphs as introduced by Brešar and Tepeh Horvat (Cage‐amalgamation...
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