Locally constrained graph homomorphisms and equitable partitions

We explore the connection between locally constrained graph homomorphisms and degree matrices arising from an equitable partition of a graph. We provide several equivalent characterizations of degree matrices. 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. 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 also these latter types of homomorphisms impose a quasiorder on degree abstracts of some of the results presented in this paper were presented at international conferences Mathematical Foundations of Computer Science 2005 and Graph-Theoretical Concepts in Computer Science 2005 and appeared in Lecture Notes in Computer Science 3618 (2005), pp. 340

• Type: Journal
• Year: 2008
• Where: EJC
• Authors: Jirí Fiala, Daniël Paulusma, Jan Arne Telle
• Keywords: Computer Science, Degree Matrices, Degree Matrix, EJC 2007, EJC 2008, Information Technology