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1. Let G = (V,E) be a graph for which all nodes have degree 5 and where G is 5-edge is connected.
a) Show that the vector x which is indexed by the edges E and for which xe = 1/5 for all e in E is in the Perfect Matching Polytope PPM.
b) Use your result in a) to show that G must have a perfect matching.
c) Show that b) may not be true if G is only 1-edge connected (but still has degree 5 everywhere) by giving an example of such a graph G which has no perfect matching.
00000000110 write in scientific notation
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An elliptical galaxy has gravitational boundaries defiend by 9x 2 +16y 2 +144z 2 =144. A black hole at the center of the galaxy is interacting with dark matter producing a radiatio
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