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It is known that for every integer $k \\geq 1$, every graph $G$ has a polynomially constructible $(2k-1,0)$-spanner of size $O(n^{1+1/k})$. This size-stretch bound is essentially optimal by the girth conjecture. It is therefore intriguing to ask if one can \"bypass\" the conjecture by settling for a multiplicative stretch o"},"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":"1404.6835","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-27T21:55:35Z","cross_cats_sorted":[],"title_canon_sha256":"073b7a8ba035d720836e4cbf291747817bc11beba5400a2fbcca51fc1898fc65","abstract_canon_sha256":"5798fd7d99535570b655e6d93c683d881d38b8032bcb6447239ed03663cd223d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:05.770030Z","signature_b64":"vCMg7JeTNvK/qMP/A/rUYB5bSy/z+V9NjcuWpt1n3mAWBE8wDaeaXd/njDsfKbyGJcNyWSSZ1XMvn/QA7mMUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c7e264befc6de2baf88639adc0fb89746848bc0b00e34347eae9e6b675e4a9c","last_reissued_at":"2026-05-18T02:53:05.769452Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:05.769452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bypassing Erd\\H{o}s' Girth Conjecture: Hybrid Stretch and Sourcewise Spanners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Merav Parter","submitted_at":"2014-04-27T21:55:35Z","abstract_excerpt":"An $(\\alpha,\\beta)$-spanner of an $n$-vertex graph $G=(V,E)$ is a subgraph $H$ of $G$ satisfying that $dist(u, v, H) \\leq \\alpha \\cdot dist(u, v, G)+\\beta$ for every pair $(u, v)\\in V \\times V$, where $dist(u,v,G')$ denotes the distance between $u$ and $v$ in $G' \\subseteq G$. 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