Continuity of the percolation threshold in randomly grown graphs
Centre for Mathematical Sciences
Lund Institute of Technology,
We consider various models of randomly grown graphs introduced and studied
previously independently. In these models the vertices and the edges are
accumulated in time according to certain rules. We study a phase transition
in these models along a parameter which refers to the mean life of an edge.
Although deleting of old edges in the uniformly grown graph changes abruptly
the properties of the model, we show that some of the macro-characteristics
of graph remain continuous. In particular, our results yield a lower bound
for the size of the largest connected component of the uniformly grown graph.