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Strong Induction, Tangled Graph
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[QUOTE="QuietMind, post: 5443196, member: 584429"] Is G2 necessarily tangled? Right now I am suspicious of G2 being considered tangled, but I can't figure out why not. My reasoning below seems to lead me to the conclusion that it is tangled: The parent graph G is said to be tangled. I think that guarantees any subgraphs be tangled, because then a graph of n nodes would have an edge leaving every set of ##\lceil n/3 \rceil## or fewer nodes. A subgraph would have fewer than n nodes, so the condition for tangleness would be the ceiling of fewer than n/3 nodes, which is assured by the parent's tangled status. But then, if G2 is tangled, by the induction hypothesis it is connected, and you're telling me the error is before that part of the proof. [/QUOTE]
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Strong Induction, Tangled Graph
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