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Our lightness bound is \\[O\\left(\\frac{\\sigma_H}{\\epsilon^3}\\log \\frac{1}{\\epsilon}\\right)\\] where $\\sigma_H = |V(H)|\\sqrt{\\log |V(H)|}$ is the sparsity coefficient of $H$-minor-free graphs. That is, it has a practical dependency on the size of the minor $H$. Our result also implies that the polynomial time approximation scheme (PTAS) for the Travelling Salesperson Problem (TSP) in $H$-minor-free graphs by Demaine, Hajiaghayi a"},"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":"1711.00821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-11-02T17:04:58Z","cross_cats_sorted":[],"title_canon_sha256":"f41f5b8db1eca8eaaf4d97b46fcb27dff3a2b5a4232395281eba0eec756b4590","abstract_canon_sha256":"1c1efe1b982f523cfcd235de155f1d8d6cb5ad29b312644cf768f03ce010e4e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:29.454695Z","signature_b64":"GCGfElc0Hn7OU/PVE8bVwI/g2BPTPwPqywCAASX+aHepbcLHcW4tHlp0ExF2yzY2dJQONOR4nWnzdAAAvqmSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa16dc47d8ac59ab39ce76d6a320f683906a16bafe2d20b70cd39798783cf67c","last_reissued_at":"2026-05-18T00:31:29.454245Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:29.454245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minor-free graphs have light spanners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Christian Wulff-Nilsen, Glencora Borradaile, Hung Le","submitted_at":"2017-11-02T17:04:58Z","abstract_excerpt":"We show that every $H$-minor-free graph has a light $(1+\\epsilon)$-spanner, resolving an open problem of Grigni and Sissokho and proving a conjecture of Grigni and Hung. 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