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The $k^+$-star packing problem is to cover as many vertices of an input graph $G$ as possible using vertex-disjoint $k^+$-stars in $G$; and given $k > t \\ge 1$, the $k^-/t$-star packing problem is to cover as many vertices of $G$ as possible using vertex-disjoint $k^-$-stars but no $t$-stars in $G$. Both problems are NP-hard for any fixed $k \\ge 2$. We present"},"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":"2411.11136","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2024-11-17T17:46:18Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"dfd1eca30ffc1ac8ad397f5f07f8af8fbd467b4d3d59ab71a3afdf0ec59b08de","abstract_canon_sha256":"16fefb0b6a5f265654f761eb61405237f3e06d93634ddf7065ea49a6c81d5a6a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:36:29.165458Z","signature_b64":"h6tPO+kXuCwoUQ7rvposIzKWfR/nwqL4gSiGoWM5OBCpxxRi9vC9YrG9bpiz/xThHTAk2kI4QnZbWrQw4dJuCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8947739863f5a274fcdc73fd166c93d14c29d16907e9620a91792a32ec51f7b1","last_reissued_at":"2026-07-05T09:36:29.164988Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:36:29.164988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximation algorithms for non-sequential star packing problems","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"An Zhang, Guohui Lin, Mengyuan Hu, Mingyang Gong, Yong Chen","submitted_at":"2024-11-17T17:46:18Z","abstract_excerpt":"For a positive integer $k \\ge 1$, a $k$-star ($k^+$-star, $k^-$-star, respectively) is a connected graph containing a degree-$\\ell$ vertex and $\\ell$ degree-$1$ vertices, where $\\ell = k$ ($\\ell \\ge k$, $1 \\le \\ell \\le k$, respectively). The $k^+$-star packing problem is to cover as many vertices of an input graph $G$ as possible using vertex-disjoint $k^+$-stars in $G$; and given $k > t \\ge 1$, the $k^-/t$-star packing problem is to cover as many vertices of $G$ as possible using vertex-disjoint $k^-$-stars but no $t$-stars in $G$. Both problems are NP-hard for any fixed $k \\ge 2$. 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