Matrix and Graph Orders Derived from Locally Constrained Graph Homomorphisms

  • Jiří Fiala
  • Daniël Paulusma
  • Jan Arne Telle
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3618)


We consider three types of locally constrained graph homomorphisms: bijective, injective and surjective. We show that the three orders imposed on graphs by existence of these three types of homomorphisms are partial orders. We extend the well-known connection between degree refinement matrices of graphs and locally bijective graph homomorphisms to locally injective and locally surjective homomorphisms by showing that the orders imposed on degree refinement matrices by our locally constrained graph homomorphisms are also partial orders. We provide several equivalent characterizations of degree (refinement) matrices, e.g. in terms of the dimension of the cycle space of a graph related to the matrix. As a consequence we can efficiently check whether a given matrix M is a degree matrix of some graph and also compute the size of a smallest graph for which it is a degree matrix in polynomial time.


Partial Order Universal Cover Regular Graph Local Constraint Surjective Homomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jiří Fiala
    • 1
  • Daniël Paulusma
    • 2
  • Jan Arne Telle
    • 3
  1. 1.Faculty of Mathematics and Physics, DIMATIA and Institute for Theoretical Computer Science (ITI)Charles UniversityPragueCzech Republic
  2. 2.Department of Computer ScienceUniversity of Durham, Science LaboratoriesDurhamEngland
  3. 3.Department of InformaticsUniversity of BergenBergenNorway

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