2024/05/01 by Adrian Rettich, Rettich, Adrian
Computer Science · Mathematics · #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Logic (math.LO) #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2405.00758
openalex publication_date 2024/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Courcelle's Theorem is an important result in graph theory, proving the existence of linear-time algorithms for many decision problems on graphs whose tree-width is bounded by a constant. The purpose of this text is twofold: to provide an explanation and step-by-step proof of Courcelle's Theorem as applied to graphs of tree-width bounded by a constant, and to show explicitly (on the example of path-width) how to apply the same principles to other graph classes. We present these topics in a way that does not assume any particular knowledge on the part of the reader except a basic understanding of mathematics and possibly the fundamentals of graph theory. Our hope is to make the topic accessible to a broader mathematical audience, to which end we have included extensive explanations and pretty pictures.