Interval Graphs are Reconstructible
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918497390428160 |
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| author | Heinrich, Irene Kiyomi, Masashi Otachi, Yota Schweitzer, Pascal |
| author_facet | Heinrich, Irene Kiyomi, Masashi Otachi, Yota Schweitzer, Pascal |
| contents | A graph is reconstructible if it is determined up to isomorphism by the multiset of its proper induced subgraphs. The reconstruction conjecture postulates that every graph of order at least 3 is reconstructible. We show that interval graphs with at least three vertices are reconstructible. For this purpose, we develop a technique to handle separations in the context of reconstruction. This resolves a major roadblock to using graph structure theory in the context of reconstruction. To apply our novel technique, we also develop a resilient combinatorial structure theory for interval graphs. A consequence of our result is that interval graphs can be reconstructed in polynomial time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02353 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interval Graphs are Reconstructible Heinrich, Irene Kiyomi, Masashi Otachi, Yota Schweitzer, Pascal Combinatorics Discrete Mathematics Data Structures and Algorithms 68R10, 68Q25 F.2.2; G.2.2 A graph is reconstructible if it is determined up to isomorphism by the multiset of its proper induced subgraphs. The reconstruction conjecture postulates that every graph of order at least 3 is reconstructible. We show that interval graphs with at least three vertices are reconstructible. For this purpose, we develop a technique to handle separations in the context of reconstruction. This resolves a major roadblock to using graph structure theory in the context of reconstruction. To apply our novel technique, we also develop a resilient combinatorial structure theory for interval graphs. A consequence of our result is that interval graphs can be reconstructed in polynomial time. |
| title | Interval Graphs are Reconstructible |
| topic | Combinatorics Discrete Mathematics Data Structures and Algorithms 68R10, 68Q25 F.2.2; G.2.2 |
| url | https://arxiv.org/abs/2504.02353 |