Infinite limits and folding

Anthony Bonato 1 Jeannette Janssen 2
1 Department of Mathematics, Wilfrid Laurier University
2 Department of Mathematics and Statistics [Canada]
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.
Keywords : massive networks duplication model infinite random graph folding adjacency property graph homomorphism
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Communication dans un congrès
Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.223-228, 2005, DMTCS Proceedings
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Anthony Bonato, Jeannette Janssen. Infinite limits and folding. Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.223-228, 2005, DMTCS Proceedings. 〈hal-01184367〉

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