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BFS-Based Canonical Codes for Generating Graphs with Constraint Programming

Authors Xiao Peng , Christine Solnon

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph enumeration
  • Computing methodologies → Artificial intelligence
Keywords
  • Graph Generation
  • Automorphisms
  • Symmetry Breaking

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Abstract

We consider the problem of generating all graphs that satisfy some given additional constraints (on vertex degrees, or cycle lengths, for example). Most previous works have proposed to generate canonical codes associated with adjacency matrices. In this paper, we consider canonical codes based on Breadth First Search (BFS), and we show how to generate them with Constraint Programming (CP): we introduce a set of basic constraints that must be satisfied by all canonical codes, thus breaking many symmetries, and we introduce a global constraint to break other symmetries. We illustrate the interest of our approach on connected claw-free cubic graphs, and show that it outperforms state-of-the-art CP and SAT Modulo Theory (SMT) approaches.

Cite As Get BibTex

Xiao Peng and Christine Solnon. BFS-Based Canonical Codes for Generating Graphs with Constraint Programming. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CP.2025.32

Author Details

Xiao Peng
  • LAAS-CNRS, Université de Toulouse, Toulouse, France
Christine Solnon
  • Univ Lyon, INSA Lyon, Inria, CITI, EA3720, 69621 Villeurbanne, France

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