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We prove that any $n$-vertex triangle-free graph has at most $3^{n/3} \\approx 1.4423^n$ maximal induced matchings, and this bound is attained by any disjoint union of copies of the complete bipartite graph $K_{3,3}$. Our result implies that all maximal induced matchings in an $n$-vertex triangle-free graph can be listed in time $O(1.4423^n)$, yielding the fastest "},"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":"1312.5180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-18T15:36:40Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"77b1ca6eb1b318263b8d902c2ae64a2484b7e3bc803c4aedce9bc70b4f6c149f","abstract_canon_sha256":"48c27aea97c8abf7e921b40232308fff958204a00131052aafc410c9aac23313"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:16.020463Z","signature_b64":"P5Hvi8nVeRVUw9Jvn2QDclXW1JcGTGfsCGhRVvndRGSqGs//El3WUTAN4XiTvzRloVgfg/Y2fxFzkh07Q4/dDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"654435190fe15af19df6b781260e39a56c8c14cfcd33f3448a472eef1cd59724","last_reissued_at":"2026-05-18T03:04:16.019801Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:16.019801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximal induced matchings in triangle-free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.CO","authors_text":"Manu Basavaraju, Pim van 't Hof, Pinar Heggernes, Reza Saei, Yngve Villanger","submitted_at":"2013-12-18T15:36:40Z","abstract_excerpt":"An induced matching in a graph is a set of edges whose endpoints induce a $1$-regular subgraph. 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