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Grid Grove is a neighborhood, with houses organized in m rows of n columns. Houses that are closest to each other are connected by a path (note that this organization follows the definition of a grid graph given in lecture). Assume that m, n 2 2. As follows from lecture, Grid Grove has mn houses and 2mn – m - n paths. It is also possible to walk to any house from any other house through some sequence of paths. To save money, the landlords want to get rid of some paths. Calculate D, the maximum number of paths that can be removed from the neighborhood without disconnecting it. Justify your answer. Then describe (informally) which D paths of the neighborhood can be removed (there is more than one such set of D paths).

Grid Grove is a neighborhood, with houses organized in m rows of n columns. Houses that are closest to each other are connected by a path (note that this organization follows the definition of a grid graph given in lecture). Assume that m, n 2 2. As follows from lecture, Grid Grove has mn houses and 2mn – m - n paths. It is also possible to walk to any house from any other house through some sequence of paths. To save money, the landlords want to get rid of some paths. Calculate D, the maximum number of paths that can be removed from the neighborhood without disconnecting it. Justify your answer. Then describe (informally) which D paths of the neighborhood can be removed (there is more than one such set of D paths).

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter2: Parallel Lines
Section2.5: Convex Polygons
Problem 41E
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Grid Grove is a neighborhood, with houses organized in m rows of n columns. Houses that are closest to each other are connected by a path (note that this organization follows the definition of a grid graph given in lecture). Assume that m, n > 2. As follows from lecture, Grid Grove has mn houses and 2mn – m -n paths. It is also possible to walk to any house from any other house through some sequence of paths. To save money, the landlords want to get rid of some paths. Calculate D, the maximum number of paths that can be removed from the neighborhood without disconnecting it. Justify your answer. Then describe (informally) which D paths of the neighborhood can be removed (there is more than one such set of D paths).
Transcribed Image Text:Grid Grove is a neighborhood, with houses organized in m rows of n columns. Houses that are closest to each other are connected by a path (note that this organization follows the definition of a grid graph given in lecture). Assume that m, n > 2. As follows from lecture, Grid Grove has mn houses and 2mn – m -n paths. It is also possible to walk to any house from any other house through some sequence of paths. To save money, the landlords want to get rid of some paths. Calculate D, the maximum number of paths that can be removed from the neighborhood without disconnecting it. Justify your answer. Then describe (informally) which D paths of the neighborhood can be removed (there is more than one such set of D paths).
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