Advertisement
Published in:
2005 | OriginalPaper | Chapter
Matrix and Graph Orders Derived from Locally Constrained Graph Homomorphisms
Authors : Jiří Fiala, Daniël Paulusma, Jan Arne Telle
Published in: Mathematical Foundations of Computer Science 2005
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
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.