2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 223228
author:  Anthony Bonato and Jeannette Janssen 

title:  Infinite limits and folding 
keywords:  massive networks, duplication model, infinite random graph, folding, adjacency property, graph homomorphism 
abstract: 
We study infinite limits of graphs generated by the
duplication model for biological networks. We prove that
with probability
1
, the sole nontrivial connected component of the
limits is unique up to isomorphism. We describe certain
infinite deterministic graphs which arise naturally from
the model. We characterize the isomorphism type and induced
subgraph structure of these infinite graphs using the
notion of dismantlability from the theory of vertex pursuit
games, and graph homomorphisms.

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reference:  Anthony Bonato and Jeannette Janssen (2005), Infinite limits and folding, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 223228 
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