Cantor-Bernstein type theorem for locally constrained graph homomorphisms

  • Authors:
  • Jiří Fiala;Jana Maxová

  • Affiliations:
  • Charles University, Faculty of Mathematics and Physics, KAM, DIMATIA and Institute for Theoretical Computer Science (ITI), Prague, Czech Republic;Charles University, Faculty of Mathematics and Physics, KAM, DIMATIA and Institute for Theoretical Computer Science (ITI), Prague, Czech Republic

  • Venue:
  • European Journal of Combinatorics - Special issue on Eurocomb'03 - graphs and combinatorial structures
  • Year:
  • 2006

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Abstract

We show that the simultaneous existence of a single locally surjective graph homomorphism between a graph G and a connected and finite graph H together with some locally injective homomorphism between the same pair of graphs assures that both homomorphisms are locally bijective.We give a short proof of this assertion which unifies previously known partial results of this form. We utilize the notion of universal cover, and relate its properties to the notion of degree refinement, which was used as a principal tool in other works.