-2
votes
1answer
42 views

Min $A=14(a^{2}+b^{2}+c^{2})+\frac{ab+bc+ac}{a^{2}b+b^{2}c+c^{2}a}$?

$a;b;c\in \mathbb{R}^+$ such that $a+b+c=1$. Find the minimum of $A=14(a^{2}+b^{2}+c^{2})+\frac{ab+bc+ac}{a^{2}b+b^{2}c+c^{2}a}$
0
votes
2answers
79 views

Bounds for maximal blowup contained in graph

In my homework, I'm asked to prove the following: By denoting $b_n(r,\epsilon)$ - the largest integer $b$ so that any graph with $(1-\frac{1}{r} +\epsilon)\frac{n^2}{2}$ edges, contains a $b$-blowup ...
5
votes
1answer
236 views

Graph with 10 nodes and 26 edges must have at least 5 triangles

This is not a homework question, but I would appreciate if people would treat this as if it were homework. I am looking for (nonspoiler) hints. I would like to prove that given any graph with 10 ...