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.

翻译：一个图如果由其所有真导出子图的多重集在同构意义下唯一确定，则称该图是可重构的。重构猜想假定每个至少包含3个顶点的图都是可重构的。我们证明顶点数至少为3的区间图是可重构的。为此，我们开发了一种在重构背景下处理分离结构的技术。这解决了在图结构理论应用于重构问题时面临的主要障碍。为了应用这一新技术，我们还为区间图建立了一个稳健的组合结构理论。我们的结果的一个推论是：区间图可以在多项式时间内完成重构。