Matrix and graph orders derived from locally constrained graph homomorphisms

Fiala, J.; Paulusma, D.; Telle, J. A.

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.

Citation

Fiala, J., Paulusma, D., & Telle, J. A. (2023, August). Matrix and graph orders derived from locally constrained graph homomorphisms. Presented at 30th International Symposium on Mathematical Foundations of Computer Science : MFCS 2005, Gdansk, Poland

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 30th International Symposium on Mathematical Foundations of Computer Science : MFCS 2005
• Start Date: Aug 29, 2023
• End Date: Sep 2, 2005
• Publication Date: 2005-08
• Deposit Date: Oct 30, 2008
• Print ISSN: 0302-9743
• Pages: 340-351
• Series Title: Lecture notes in computer science
• Series Number: 3618
• Series ISSN: 0302-9743
• Book Title: Mathematical foundations of computer science 2005 : 30th International Symposium, MFCS 2005, Gdansk, Poland, 29 August 29-2September 2005 ; proceedings
• DOI: https://doi.org/10.1007/11549345_30
• Keywords: Bijective, Injective, Surjective, Partial orders.
• Public URL: https://durham-repository.worktribe.com/output/1164110
• Additional Information: 29 August - 2 September, 2005.