In addition to Sam Nead's [answer](https://mathoverflow.net/a/463005/2383), which is about how to get started in math research, I want to direct the OP's attention to many lists of open problems in graph theory. For someone with a background in the IMO, who likes problem solving, this is a concrete way to get into research. If you manage to solve one of these open problems, you can publish the solution (there are several MO threads about undergrad math journals that you might find useful, e.g., [this one][1]). 

Ok, lists of open problems in graph theory:

http://dimacs.rutgers.edu/~hochberg/undopen/graphtheory/graphtheory.html

http://www.openproblemgarden.org/category/graph_theory

https://mathoverflow.net/questions/191495/collection-of-conjectures-and-open-problems-in-graph-theory

https://mathoverflow.net/questions/225870/open-problems-for-undergraduates

https://mathoverflow.net/questions/27716/does-there-exist-a-comprehensive-compilation-of-erdoss-open-problems

https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics#Graph_theory

https://mathweb.ucsd.edu/~erdosproblems/

https://dwest.web.illinois.edu/ (two links to lists of open problems)

[Spirkl - Open problems for the 2020 Barbados graph theory workshop](https://sites.google.com/site/sophiespirkl/open-problems/2020-open-problems-for-the-barbados-graph-theory-workshop)

[Open problems for the Barbados graph theory workshop 2017](https://web.math.princeton.edu/~pds/barbados17/openproblems2017.pdf)

Open problems in spectral graph theory:
https://arxiv.org/abs/2305.10290 and https://arxiv.org/abs/1907.04349

https://www.cs.upc.edu/~sedthilk/grow/Open_Problems_GROW_2013.pdf

[Nguyen - Open problems for the second 2022 Barbados workshop](https://web.math.princeton.edu/~tunghn/2022openproblems.pdf)

https://www.quora.com/What-are-some-interesting-unsolved-problems-in-graph-theory-or-topology

[Stout - Some open problems and conjectures](https://web.eecs.umich.edu/~qstout/constantques.html)

[Aldous - Some of my favorite open problems](https://www.stat.berkeley.edu/~aldous/Talks/OP2018.pdf)

[Steinerberger - Some open problems](https://faculty.washington.edu/steinerb/openproblems.pdf)

[Kaul - Some open problems](http://www.math.iit.edu/~kaul/talks/OpenProblems.pdf)

[Gera - Graph theory - Favorite conjectures and open problems - 1](https://www.semcoop.com/graph-theory-favorite-conjectures-and-open-problems)

[Gera - Graph theory - Favorite conjectures and open problems - 2](https://doi.org/10.1007/978-3-319-97686-0)

[Simonovits - Important open problems in extremal graph theory](https://old.renyi.hu/~miki/XianSlides2021f.pdf)


  [1]: https://mathoverflow.net/questions/365808/publishing-undergraduate-research "Publishing undergraduate research"