{"paper":{"title":"Hypomorphy of graphs up to complementation","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"G\\'erard Lopez (IML), Hamza Si Kaddour (ICJ), Jamel Dammak, Maurice Pouzet (ICJ)","submitted_at":"2006-01-06T15:01:44Z","abstract_excerpt":"Let $V$ be a set of cardinality $v$ (possibly infinite). Two graphs $G$ and $G'$ with vertex set $V$ are {\\it isomorphic up to complementation} if $G'$ is isomorphic to $G$ or to the complement $\\bar G$ of $G$. Let $k$ be a non-negative integer, $G$ and $G'$ are {\\it $k$-hypomorphic up to complementation} if for every $k$-element subset $K$ of $V$, the induced subgraphs $G\\_{\\restriction K}$ and $G'\\_{\\restriction K}$ are isomorphic up to complementation. A graph $G$ is {\\it $k$-reconstructible up to complementation} if every graph $G'$ which is $k$-hypomorphic to $G$ up to complementation is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601118","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}