Continuity of the percolation threshold in randomly grown graphs

Tatyana Turova

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
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.
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