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The Maximum Degree and Diameter Bounded Subgraph Problem (MaxDDBS) asks:given a host graph G, a bound on maximum degree \Delta, and a diameter D, whatis the largest subgraph of the host graph with degree bounded by \Delta anddiameter bounded by D? In this paper, we investigate this problem when the hostgraph is the k-dimensional mesh. We provide lower bounds for the size of thelargest subgraph of the mesh satisfying MaxDDBS for all k and \Delta > 3 thatagree with the known upper bounds up to the first two terms, and show that for\Delta = 3, the lower bounds are at least the same order of growth as the upperbounds.

Sharper Lower Bounds in the Maximum Degree and Diameter Bounded Subgraph Problem in the Mesh