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