{"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 $\\{b,x\\}\\in E$. For example, $\\emptyset$, $\\{x\\}(x\\in V)$ and $V$ are intervals of $G$, called trivial intervals. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3074","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"}