A Critical Point for Random Graphs with a Given Degree Sequence

  title={A Critical Point for Random Graphs with a Given Degree Sequence},
  author={Michael Molloy and Bruce A. Reed},
  journal={Random Struct. Algorithms},
Given a sequence of non-negative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n ver-tices of degree i. Essentially, we show that if P i(i?2) i > 0 then such graphs almost surely have a giant component, while if P i(i?2) i < 0 then almost surely all components in such graphs are small. We can apply these results to G n;p ; G n;M , and other well-known models of random graphs. There are also applications related to the chromatic number of sparse… CONTINUE READING
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