User3419
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 Oct 18 comment Threshold of connectivity in a random graph So how do you arrive at $(1-p) \leqslant \mathrm{e}^{-p}$? Or is it another inequality? Oct 18 comment Threshold of connectivity in a random graph Thanks very much for your reply once again! For the second equation I understand how it works (which confirmed my understanding) but still I do not see the connection between the first one, the line that concludes the formal proof, and the inequalities I've provided that should facilitate arriving at the proof. Could you, please, elaborate on it? Oct 15 comment Threshold of connectivity in a random graph Well, as I stated in the post, I cannot arrive at the last line of the proof. I've reported my derivations which lead me nowhere w.r.t. the proof, so the question is basically, how given the two inequalities (before my own intervention after the $\therefore$ symbol) the line of the proof can be obtained? Apr 30 comment Combination of splitting elements into pairs @user6312, thank you! Apr 29 comment Combination of splitting elements into pairs I see. Thanks very much! Apr 28 comment Problem about number of vertices of a graph @Jim Conant and @lhf: Thank you! Apr 28 comment Problem about number of vertices of a graph Thanks very much for the explanation! Apr 10 comment Permutation/Combination of x,y and z moves 12 was a typo. Fixed now. Excuse me, I don't understand what you mean with your second question. Could you, please, be more specific? Apr 9 comment Permutation/Combination of x,y and z moves Thanks! Indeed it is a very good alternative. Apr 9 comment Permutation/Combination of x,y and z moves Now I get it. I tried to approach it analogically starting with y, then z, and leaving x for the end. I got the same answer $\binom{13}{4} \binom{9}{7} = 25740$. Thank you!