Mehrabian, Mitsche, and Pralat showed that any -vertex graph with a good edge-labelling has at most edges, and that for each there is an -vertex graphs with a good edge-labelling having edges.

http://arxiv.org/abs/1211.2641

## First question (almost) solved

Mehrabian, Mitsche, and Pralat showed that any -vertex graph with a good edge-labelling has at most edges, and that for each there is an -vertex graphs with a good edge-labelling having edges.

http://arxiv.org/abs/1211.2641