Let $G$ be a graph with $a\choose 2$ edges (and an arbitrary number of vertices). Is it true that it has at most $a\choose 3$ triangles? Context: this continues the question Number of triangles in a ...
What is the minimum number of edges of graph $G$, so that every tree of size $n$ is a subgraph of $G$? I personally managed to find a lower bound of $c n \log n $ and an upper bound of $C n \log ...
I'm reading the Extremal Graph Theory book by Bollobás, and I'm stuck at the definition of 'compatible vertices'. It's here at the bottom of p.13 It says : "Call two vertices compatible if every ...
Find the smallest positive constant $c$ satisfying: For any simple graph $G=G(V,E)$, if $|E|\geq c|V|$, then $G$ contains $2$ cycles with no common vertex, and one of them contains a chord. Note: The ...