Graph theory - complete subgraphs

Gh0stZA
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Hi everyone.

If we have a graph G of order n >= 4, and every vertex v in G has degree (2n+1)/3, prove that every edge in G is part of a complete subgraph of order 4.
I know this holds for complete graphs, I've proved that by induction. But how can I prove it for graphs which aren't complete? And what is the significance of (2n+1)/3? If a vertex has that degree, does it have some property I should immediately spot?
 
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Sorry to bump, any help please?
 

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