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arXiv · 2504.02353

Interval Graphs are Reconstructible

Irene Heinrich·Masashi Kiyomi·Yota Otachi·Pascal Schweitzer
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Abstract

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.

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BibTeXRIS

Irene Heinrich, Masashi Kiyomi, Yota Otachi, Pascal Schweitzer. 2025-04-03. Interval Graphs are Reconstructible. https://arxiv.org/abs/2504.02353

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