Bi-resolving Graph Homomorphisms and Extensions of Bi-closing codes

Authors:
Uijin Jung;In-Je Lee
Affiliations:
Department of Mathematics, Ajou University, Suwon, South Korea 443-749;The Jesuit Novitiate of St. Stanislaus in Korea, Suwon, South Korea
Venue:
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Year:
2013

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Abstract

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.