A note on percolation theory
Open Access
- 1 February 1982
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 15 (2) , 605-610
- https://doi.org/10.1088/0305-4470/15/2/027
Abstract
In percolation theory the critical probability Pc(G) of an infinite connected graph G is defined as the supremum of those values of the occupation probability for which only finite clusters occur. An interesting question is the following: is each number between 0 and 1 the critical probability of some graph? It is shown that the answer is positive. A remarkable intermediate result is that for an important class of graphs the following holds: for each p>or=Pc(G) there exists a subgraph of G with critical probability equal to p.Keywords
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