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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!

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    $\begingroup$ PhD projects should not be sought by some kind of online comparison shopping. Why not pick up a book on random graphs and read some of it and try to understand some of it? $\endgroup$ – Yemon Choi Jan 19 '19 at 23:49
  • $\begingroup$ @YemonChoi Yes, you're right. I have read several books, papers and ... and have some general ideas for a PhD project, but I would like to know the ideas of expert people! $\endgroup$ – Henry Zagreb Jan 19 '19 at 23:55
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    $\begingroup$ Do you have a thesis adviser who can suggest some problems? If not, how will you be supervised if you write a thesis on random graphs? $\endgroup$ – Richard Stanley Jan 20 '19 at 2:06
  • $\begingroup$ @RichardStanley My advisor is not expert in this area, but he has given me this freedom to work on my own interests. $\endgroup$ – Henry Zagreb Jan 20 '19 at 19:06
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Check out the Open Problem Garden, which lists this problem:


          Bukh
          Due to MO user @BorisBukh.


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