Suppose that, in addition to edge capacities, a flow network has vertex capacities. that is each vertex vv has a limit l(v)l(v) on how much flow can pass though vv. show how to transform a flow network g = (v, e)g=(v, e) with vertex capacities into an equivalent flow network g' = (v', e')g ′ =(v ′ ,e ′ ) without vertex capacities, such that a maximum flow in g'g ′ has the same value as a maximum flow in gg. how many vertices and edges does g'g ′ have?

that would be my answer.

there is no universally accepted definition of art. although commonly used to describe something of beauty, or a skill which produces an aesthetic result, there is no clear line in principle between (say) a unique piece of handmade sculpture, and a mass-produced but visually attractive item. we might say that art requires thought - some kind of creative impulse - but this raises more questions: for example, how much thought is required? if someone flings paint at a canvas, hoping by this action to create a work of art, does the result automatically constitute art?