Looking for an interesting graph theory open problem to write a paper on

--- here's an example, however it's not recommended for undergrads, but ya...

The deck of a graph $ G $ is the multiset consisting of all unlabelled subgraphs obtained from $ G $ by deleting a vertex in all possible ways (counted according to multiplicity).
Conjecture If two graphs on $ \ge 3 $ vertices have the same deck, then they are isomorphic.

more info on this problem https://en.wikipedia.org/wiki/Reconstruction_conjecture

Question

Looking for an interesting graph theory open problem to write a paper on

--- here's an example, however it's not recommended for undergrads, but ya...

The deck of a graph $ G $ is the multiset consisting of all unlabelled subgraphs obtained from $ G $ by deleting a vertex in all possible ways (counted according to multiplicity).
Conjecture   If two graphs on $ \ge 3 $ vertices have the same deck, then they are isomorphic.

more info on this problem https://en.wikipedia.org/wiki/Reconstruction_conjecture