Geodesic
Bandwidth reduction in rectangular grids
Algebra and discrete mathematics, no. 2 (2007), pp. 1-15.

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We show that the bandwidth of a square two-dimensional grid of arbitrary size can be reduced if two (but not less than two) edges are deleted. The two deleted edges may not be chosen arbitrarily, but they may be chosen to share a common endpoint or to be non-adjacent. We also show that the bandwidth of the rectangular $n \times m$ ($n\leq m$) grid can be reduced by $k$, for all $k$ that are sufficiently small, if $m-n+2k$ edges are deleted.
Keywords: linear bandwidth, rectangular grid. 
@article{ADM_2007_2_a1,
     author = {Titu Andreescu and Water Stromquist and Zoran \v{S}un{\'\i}c},
     title = {Bandwidth reduction in rectangular grids},
     journal = {Algebra and discrete mathematics},
     pages = {1--15},
     publisher = {mathdoc},
     number = {2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2007_2_a1/}
}
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Titu Andreescu; Water Stromquist; Zoran Šuníc. Bandwidth reduction in rectangular grids. Algebra and discrete mathematics, no. 2 (2007), pp. 1-15. http://geodesic.mathdoc.fr/item/ADM_2007_2_a1/