Anthony Bonato ; Jeannette Janssen

Infinite limits and folding
dmtcs:3410 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2005,
DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

https://doi.org/10.46298/dmtcs.3410
Infinite limits and folding
Authors: Anthony Bonato ^{1}; Jeannette Janssen ^{2}
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Anthony Bonato;Jeannette Janssen
1 Department of Mathematics, Wilfrid Laurier University
2 Department of Mathematics and Statistics [Canada]
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.