Suppose G is simple with degree sequence $d_1 \leq d_2\leq ....\leq d_n$, and for $k \leq n-d_n-1$, $d_k \geq k$. Show G is connected.
I posted this question before, and got an answer, but I couldn't understand it fully. (Especially about why $d_1 \geq n-d_n-1$.) Here's a link to that answer. Graph theory (Graph Connectivity) Anybody, help me, please.