I am a 10th grader and I'm very interested in mathematics. As of now, I'm into math contests and I take great pleasure in solving problems from contests such as the AIME/USAMO/IMO. These only require high school level mathematical knowledge and are based mainly on problem-solving.

However, since a few months, advanced mathematics has caught my attention and I find unsolved problems to be very interesting, such as Brocard's Problem of $n!+1$ being a perfect square and Andrica's Conjecture of prime number gaps. I can understand all such problems well, but when I try and read the existing papers on the conjecture, I barely understand anything because of my limited knowledge. Until now, I have been good at math olympiads and general problem-solving in these contests, but I understand that this is another level of mathematics and it would require a far greater background than I have right now.

My dream is to do research and make some substantial progress on such problems, and at first glance, problems in graph theory seem the most appealing to me, especially after the minimal introduction I had to it through math contest problems.

So, which textbooks should I read in order to build a solid foundation for Graph Theory?

I wish to build enough background so that I can at least understand open problems in the field and understand the existing work done on them.