A spanning subgraph S = (V, E') of a connected simple graph G = (V, E ) is a f(x)-spanner if for any pair of nodes u and v, ds(u, v) 5 f(d& v)), where do and ds are the usual distance functions in graphs G and S, respectively. We are primarily interested in (t + x)-spanners, which we refer to as additive spanners. We construct low-degree additive spanners for X-trees, pyramids, and multidimensional grids. We prove, for arbitrary t > 0, that to determine whether a given graph G has an additive spanner with no more than m edges is NP-complete. 0 1993 by John Wiley & Sons, Inc.
This paper considers representations of graphs as rectanglevisibility graphs and as doubly linear graphs. These are, respectively, graphs whose vertices are isothetic rectangles in the plane with adjacency determined by horizontal and vertical visibility, and graphs that can be drawn as the union of two straight-edged planar graphs. We prove that these graphs have, with n vertices, at most 6n-20 (resp., 6n -18) edges, and we provide examples of these graphs with 6n-20 edges for each n > g.
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