The maximum degree and diameter-bounded subgraph in the mesh

Authors:
Mirka Miller;Hebert Pérez-Rosés;Joe Ryan
Affiliations:
Department of Software Engineering and Computer Science, The University of Newcastle, Australia and Department of Informatics, King's College, London, UK and Department of Mathematics, University ...;Department of Software Engineering and Computer Science, The University of Newcastle, Australia;Department of Software Engineering and Computer Science, The University of Newcastle, Australia
Venue:
Discrete Applied Mathematics
Year:
2012

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Abstract

The problem of finding the largest connected subgraph of a given undirected host graph, subject to constraints on the maximum degree @D and the diameter D, was introduced in Dekker et al. (2012) [1], 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,@D=4 and k=2,@D=3, we give constructions that result in sharper lower bounds.