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A graph whose intervals are trivial is indecomposable; otherwise, it is decomposable. According to Ille, the indecomposability graph of an undirected indecomposable graph $G$ is the graph $\\mathbb I(G)$ whose vertices are those of $G$ and edges are the unordered pairs of distinct vertices $\\{x,y\\}$ such that the induced subgra"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1308.3074","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-14T09:51:16Z","cross_cats_sorted":[],"title_canon_sha256":"e74f33b321d4c462d135cfd736751028ca313c4ca05878de6f27dab0018b5b6e","abstract_canon_sha256":"f231cfced9c8c7a1614500f58d6f04c10dab5569137b2ed5116477fc37d7f3b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:56.730681Z","signature_b64":"Ng1rJf6v3ZyLafD+6ifk6G0Tn2Bz9lDCdiO0rqSdRmzGrcJSGh+miJ40CNBi1fMV5FgsvHyrlXeI8t+DoibgCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65dddca1470e73cc6e578618938cb993965df609ac0e90ad87d3ac4ed08222c4","last_reissued_at":"2026-05-18T03:15:56.729903Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:56.729903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graphs whose indecomposability graph is 2-covered","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Imed Boudabbous, Rim Ben Hamadou","submitted_at":"2013-08-14T09:51:16Z","abstract_excerpt":"Given a graph $G=(V,E)$, a subset $X$ of $V$ is an interval of $G$ provided that for any $a, b\\in X$ and $ x\\in V \\setminus X$, $\\{a,x\\}\\in E$ if and only if $\\{b,x\\}\\in E$. 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