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for questions involving inequalities, upper and lower bounds.
4
votes
Accepted
Forbidden Tripartite Graphs
The Erdos-Stone theorem is the reference you are looking for.
For every tripartite graph $G$, the number of edges in an $n$-vertex graph that guarantees $G$ as a subgraph is $n^2/4 + o(n^2)$. It is e …
3
votes
Accepted
Combinatorial Euclidean geometry problem
Since any graph with $d+1$ vertices can be realized as a unit distance graph in $\mathbb{R}^d$, with remaining distances smaller than $1$ (and arbitrarily close to 1), the question is then equivalent …