Courcelle's Theorem: A Self-Contained Proof and a Path-Width Variant
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916231924154368 |
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| author | Rettich, Adrian |
| author_facet | Rettich, Adrian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00758 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Courcelle's Theorem: A Self-Contained Proof and a Path-Width Variant Rettich, Adrian Combinatorics Logic 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. |
| title | Courcelle's Theorem: A Self-Contained Proof and a Path-Width Variant |
| topic | Combinatorics Logic |
| url | https://arxiv.org/abs/2405.00758 |