Bi-resolving Graph Homomorphisms and Extensions of Bi-closing codes
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Given two graphs G and H, there is a bi-resolving (or bi-covering) graph homomorphism from G to H if and only if their adjacency matrices satisfy certain matrix relations. We investigate the bi-covering extensions of bi-resolving homomorphisms and give several sufficient conditions for a bi-resolving homomorphism to have a bi-covering extension with an irreducible domain. Using these results, we prove that a bi-closing code between subshifts can be extended to an n-to-1 code between irreducible shifts of finite type for all large n.
KeywordsCovering Resolving Subamalgamation matrix Covering extension Bi-closing Shift of finite type
Mathematics Subject Classification (2000)37B10 05C50 05C70 37B40
This paper was written during the authors’ graduate studies. We would like to thank our advisor Sujin Shin for her encouragement and good advice. We thank the referee for thorough suggestions which simplified and clarified many proofs, and Mike Boyle for comments which improved the exposition. The first named author was partially supported by TJ Park Postdoctoral Program. This work was also supported by the second stage of the Brain Korea 21 Project, The Development Project of Human Resources in Mathematics, KAIST in 2009.
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