User blog comment:Wythagoras/Results of the First International Googological Olympiad/@comment-1605058-20150223183919

Mistakes in your proof of 2.:

"\(H\) is by definition not homeomorphically embeddable into G or earlier graphs" should be other way around - no earlier graph is homeomorphically embeddable into latter one.

"any graph without edges is not homeomorphically embeddable into a graph with edges" should be other way around too.

In first paragraph, H must be choosen to be the first graph with edges after G - otherwise the following sequence is counterexample: G=(5 dots), K4, H=K3.