Give an example of a connected graph where α(G) =100 and β(G) = 200 So I need to find a form of a graph such that its vertex cover is twice that of its matching, but I am running into problems brainstorming, I know K3 is of this form, but not one at such a magnitude.
You are on the right track, just keep going: what if you take a slightly larger complete graph? Specifically, what if you take a $K_{101}$?