The Maximum Degree-and-Diameter-Bounded Subgraph in the Mesh
Abstract
The problem of finding the largest connected subgraph of a given undirected host graph, subject to constraints on the maximum degree $\Delta$ and the diameter $D$, was introduced in \cite{maxddbs}, 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 $k=3, \Delta = 4$ and $k=2, \Delta = 3$, we give constructions that result in sharper lower bounds.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2012
- DOI:
- 10.48550/arXiv.1203.4069
- arXiv:
- arXiv:1203.4069
- Bibcode:
- 2012arXiv1203.4069M
- Keywords:
-
- Mathematics - Combinatorics;
- Computer Science - Discrete Mathematics;
- 05C35 (Primary) 05C12;
- 05C90;
- 68R10;
- 95C15 (Secondary)
- E-Print:
- accepted, 18 pages, 7 figures