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NSWMaths Standard 2Quick questions
Year 12: Networks
Quick questions on Network flow and the maximum-flow minimum-cut theorem for HSC Maths Standard 2
3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is flow must be conserved at every vertex?Show answer
At every vertex except the source and the sink, whatever flows in must flow out. Water does not pile up at a junction or appear from nowhere. So if kilolitres per minute arrive at vertex , then must leave . This is conservation of flow, and it is why a single narrow edge anywhere along a route throttles the whole route: the flow that squeezes through the narrow edge is all that can continue past it.
What is finding the maximum flow by inspection?Show answer
For a small network you can find the maximum flow by eye, building it from paths:
What is the maximum-flow minimum-cut theorem?Show answer
Every cut is a complete barrier, so the flow can never beat the capacity of any single cut. The tightest barrier, the minimum cut, is therefore the true ceiling, and the theorem says that ceiling is always reached.
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