The prompt is to find the number of edges of graph with $36$ vertices given that from every $4$ vertices, at least $2$ of them have to have an edge between them. We must prove that the graph G has at least 105 edges or find some non-trivial lower limit on the number of edges.
If we join $2$ vertices of all the $36$ vertices, we are left with $18$ edges, how is this possible, how should I go on about solving a problem like this? I know that $2|E| = deg(v)$ by handshake theorem, how should I find the degree of each vertex here?