I am trying to find a good lower bound for chromatic number of one graphfamily of graphs. I'm curious what are the known lower bounds for chromatic number. There are two obvious: $\chi(G) \geq \omega(G)$ and $\chi(G) \geq n / \alpha(G)$. One can also employ fancy Lovasz theta-function.
Chromatic number of Kneser graph can be obtained by the means of topological combinatorics (particularly, using Borsuk-Ulam theorem). But it is not clear if this method is general enough.
So, what are the more or less general techniques for lowerbounding chromatic number?
