In addition to Sam Nead's answer, 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).

Ok, lists of open problems in graph theory:

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

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

Collection of conjectures and open problems in graph theory

Open Problems for Undergraduates

Does there exist a comprehensive compilation of Erdos's 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)

https://sites.google.com/site/sophiespirkl/open-problems/2020-open-problems-for-the-barbados-graph-theory-workshop

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

https://web.math.princeton.edu/~tunghn/2022openproblems.pdf

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

https://web.eecs.umich.edu/~qstout/constantques.html

https://www.stat.berkeley.edu/~aldous/Talks/OP2018.pdf

https://faculty.washington.edu/steinerb/openproblems.pdf

http://www.math.iit.edu/~kaul/talks/OpenProblems.pdf

https://www.semcoop.com/graph-theory-favorite-conjectures-and-open-problems

https://link.springer.com/book/10.1007/978-3-319-97686-0

https://old.renyi.hu/~miki/XianSlides2021f.pdf

In addition to Sam Nead's answer, 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).

Ok, lists of open problems in graph theory:

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

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

Collection of conjectures and open problems in graph theory

Open Problems for Undergraduates

Does there exist a comprehensive compilation of Erdos's 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

Open problems for the Barbados graph theory workshop 2017

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

Stout - Some open problems and conjectures

Aldous - Some of my favorite open problems

Steinerberger - Some open problems

Kaul - Some open problems

Gera - Graph theory - Favorite conjectures and open problems - 1

Gera - Graph theory - Favorite conjectures and open problems - 2

Simonovits - Important open problems in extremal graph theory