{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7OOSLQSNHEAPIQXYZNRMGWMNKM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4037801296020bc6bb7a1e1d1a2d9715c84fdfa0e12590f9d2c83dce69a10eea","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-13T08:02:41Z","title_canon_sha256":"85869b70f7d03e38c885379dd9b8804a85ea9ad84d7c7dae0230880cce9da6a7"},"schema_version":"1.0","source":{"id":"1510.03564","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03564","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03564v1","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03564","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"pith_short_12","alias_value":"7OOSLQSNHEAP","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7OOSLQSNHEAPIQXY","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7OOSLQSN","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:d80b9be7ff7e386beac46ad0d2bace4995e8985111c159784479164e9174f279","target":"graph","created_at":"2026-05-18T01:30:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let integers $r\\ge 2$ and $d\\ge 3$ be fixed. Let ${\\cal G}_d$ be the set of graphs with no induced path on $d$ vertices. We study the problem of packing $k$ vertex-disjoint copies of $K_{1,r}$ ($k\\ge 2$) into a graph $G$ from parameterized preprocessing, i.e., kernelization, point of view. We show that every graph $G\\in {\\cal G}_d$ can be reduced, in polynomial time, to a graph $G'\\in {\\cal G}_d$ with $O(k)$ vertices such that $G$ has at least $k$ vertex-disjoint copies of $K_{1,r}$ if and only if $G'$ has. Such a result is known for arbitrary graphs $G$ when $r=2$ and we conjecture that it ho","authors_text":"Anders Yeo, Bin Sheng, Florian Barbero, Gregory Gutin, Mark Jones","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-13T08:02:41Z","title":"Linear-Vertex Kernel for the Problem of Packing $r$-Stars into a Graph without Long Induced Paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03564","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ce1b3c25b53a6c1e74e62a1bbf152d44e8cde571b593c9595b1d8018a8ae5134","target":"record","created_at":"2026-05-18T01:30:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4037801296020bc6bb7a1e1d1a2d9715c84fdfa0e12590f9d2c83dce69a10eea","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-13T08:02:41Z","title_canon_sha256":"85869b70f7d03e38c885379dd9b8804a85ea9ad84d7c7dae0230880cce9da6a7"},"schema_version":"1.0","source":{"id":"1510.03564","kind":"arxiv","version":1}},"canonical_sha256":"fb9d25c24d3900f442f8cb62c3598d530e363a13f308fad77ed9507b1a36ab2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb9d25c24d3900f442f8cb62c3598d530e363a13f308fad77ed9507b1a36ab2e","first_computed_at":"2026-05-18T01:30:16.804405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:16.804405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HuLUvQvsI3Krx/FhLHoL92rciUtwSnYqoLxNsd3JM7c1zlw2NkaRP8/HizxKXm++FXvsRwIkzH5XN+tMj5JnDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:16.804997Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03564","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce1b3c25b53a6c1e74e62a1bbf152d44e8cde571b593c9595b1d8018a8ae5134","sha256:d80b9be7ff7e386beac46ad0d2bace4995e8985111c159784479164e9174f279"],"state_sha256":"2ad66420efafb2530b656a70fbe26927518ee75ea3afcde633c4f157b7846e91"}