Tree Independence Number IV. Even-hole-free Graphs
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929418433200128 |
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| author | Chudnovsky, Maria Gartland, Peter Hajebi, Sepehr Lokshtanov, Daniel Spirkl, Sophie |
| author_facet | Chudnovsky, Maria Gartland, Peter Hajebi, Sepehr Lokshtanov, Daniel Spirkl, Sophie |
| contents | We prove that the tree independence number of every even-hole-free graph is at most polylogarithmic in its number of vertices. More explicitly, we prove that there exists a constant c>0 such that for every integer n>1 every n-vertex even-hole-free graph has a tree decomposition where each bag has stability (independence) number at most c log^10 n. This implies that the Maximum Weight Independent Set problem, as well as several other natural algorithmic problems that are known to be NP-hard in general, can be solved in quasi-polynomial time if the input graph is even-hole-free. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08927 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tree Independence Number IV. Even-hole-free Graphs Chudnovsky, Maria Gartland, Peter Hajebi, Sepehr Lokshtanov, Daniel Spirkl, Sophie Combinatorics Discrete Mathematics Data Structures and Algorithms We prove that the tree independence number of every even-hole-free graph is at most polylogarithmic in its number of vertices. More explicitly, we prove that there exists a constant c>0 such that for every integer n>1 every n-vertex even-hole-free graph has a tree decomposition where each bag has stability (independence) number at most c log^10 n. This implies that the Maximum Weight Independent Set problem, as well as several other natural algorithmic problems that are known to be NP-hard in general, can be solved in quasi-polynomial time if the input graph is even-hole-free. |
| title | Tree Independence Number IV. Even-hole-free Graphs |
| topic | Combinatorics Discrete Mathematics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2407.08927 |