In real analysis, Bernoulli's inequality (named after Jacob Bernoulli) is an inequality that approximates exponentiations of 1 + x.
The inequality states that
:(1 + x)^r \geq 1 + rx\!
for every integer r ≥ 0 and every real number x ≥ −1. If the exponent r is even, then the inequality is valid for all real numbers x. The strict version of the inequality reads
:(1 + x)^r > 1 + rx\!
for every integer r ≥ 2 and every real number x ≥ −1 with x ≠0.
Bernoulli's inequality is often used as the crucial step in the proof o...
I've proved that every nontrivial tree has at least two maximal indepndent sets, with equality only for stars via the bipartition of the trees.
I am trying to extend that proof to general graphs, and I think the following is correct:
Every connected graph G with $diam(G)\ge 2$ has at least t...
