Matrix and graph orders derived from locally constrained graph homomorphisms

  • Authors:

  • Jiří Fiala;Daniël Paulusma;Jan Arne Telle

  • Affiliations:

  • Faculty of Mathematics and Physics, DIMATIA and Institute for Theoretical Computer Science (ITI), Charles University, Prague, Czech Republic;Department of Computer Science, University of Durham, Science Laboratories, Durham, England;Department of Informatics, University of Bergen, Bergen, Norway

  • Venue:
  • MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
  • Year:
  • 2005

Quantified Score

Hi-index 0.00

Visualization

Abstract

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.