I am a PhD student in mathematics. I'm interested in probabilistic methods in combinatorics and especially random graphs. I am looking for an open problem in this area for my PhD proposal. I know that there are many open problems and conjectures, but I would like to find a "good" problem such that I can get some results during my PhD. It would be very helpful for me if you could suggest a bunch of open problems. Thank you!
Check out the Open Problem Garden, which lists this problem:
Due to MO user @BorisBukh.