The problem of finding the largest connected subgraph of a given undirected host graph, subject to constraints on the maximum degree Δ and the diameter D, was introduced in Dekker et al. (2012) , as a generalization of the Degree-Diameter Problem. A case of special interest is when the host graph is a common parallel architecture. Here we discuss the case when the host graph is a k-dimensional mesh. We provide some general bounds for the order of the largest subgraph in arbitrary dimension k, and for the particular cases of k=3,Δ=4 and k=2,Δ=3, we give constructions that result in sharper lower bounds. © 2012 Elsevier B.V. All rights reserved.
Miller, M., Pérez-Rosés, H., & Ryan, J. (2012). The maximum degree and diameter-bounded subgraph in the mesh. Discrete Applied Mathematics, 160(12), 1782–1790. https://doi.org/10.1016/j.dam.2012.03.035