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math.CO2020
Spanning trees at the connectivity threshold
Yahav Alon, Michael Krivelevich, Peleg Michaeli
We present an explicit connected spanning structure that appears in a random graph just above the connectivity threshold with high probability.
math.CO2020
Cycle lengths in sparse random graphs
Yahav Alon, Michael Krivelevich, Eyal Lubetzky
We study the set of lengths of all cycles that appear in a random -regular on vertices for a fixed , as well as in Erdős--Rényi random graphs on $…