# Multi-source invasion percolation on the complete graph

@inproceedings{AddarioBerry2022MultisourceIP, title={Multi-source invasion percolation on the complete graph}, author={Louigi Addario-Berry and Jordan Barrett}, year={2022} }

. We consider invasion percolation on the randomly-weighted complete graph K n , started from some number k ( n ) of distinct source vertices. The outcome of the process is a forest consisting of k ( n ) trees, each containing exactly one source. Let M n be the size of the largest tree in this forest. Logan, Molloy and Pralat [23] proved that if k ( n ) =n 1 = 3 ! 0 then M n =n ! 1 in probability. In this paper we prove a complementary result: if k ( n ) =n 1 = 3 ! 1 then M n =n ! 0 in…

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