{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NRHMKCIYH4YANMME2BLGDQJON3","short_pith_number":"pith:NRHMKCIY","schema_version":"1.0","canonical_sha256":"6c4ec509183f3006b184d05661c12e6ee7a17829432807dfab0dfb439a912577","source":{"kind":"arxiv","id":"1707.04297","version":1},"attestation_state":"computed","paper":{"title":"The size-Ramsey number of powers of paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Barnaby Roberts, Damian Reding, Dennis Clemens, Guilherme Oliveira Mota, Matthew Jenssen, Natasha Morrison, Yoshiharu Kohayakawa","submitted_at":"2017-07-13T20:14:06Z","abstract_excerpt":"Given graphs $G$ and $H$ and a positive integer $q$ say that $G$ is $q$-Ramsey for $H$, denoted $G\\rightarrow (H)_q$, if every $q$-colouring of the edges of $G$ contains a monochromatic copy of $H$. The size-Ramsey number $\\hat{r}(H)$ of a graph $H$ is defined to be $\\hat{r}(H)=\\min\\{|E(G)|\\colon G\\rightarrow (H)_2\\}$. Answering a question of Conlon, we prove that, for every fixed $k$, we have $\\hat{r}(P_n^k)=O(n)$, where $P_n^k$ is the $k$-th power of the $n$-vertex path $P_n$ (i.e. , the graph with vertex set $V(P_n)$ and all edges $\\{u,v\\}$ such that the distance between $u$ and $v$ in $P_n"},"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":"1707.04297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-13T20:14:06Z","cross_cats_sorted":[],"title_canon_sha256":"31c55111ef5fd7c61775d9206fea23d3cbfe76593737ee30873ce423851a6d73","abstract_canon_sha256":"afe4212eb46670544eac987518d4b3bcec05dbf7ac16f3d42f64b3161b334646"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:18.746056Z","signature_b64":"5usF1qI9CJ0nQBgtqBSQpvdGba8c6I4zIQmy4b4Q+T2GH6B41wXrIYVybrVH9vgymCvTEMTcKCuz6wMN5VriDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c4ec509183f3006b184d05661c12e6ee7a17829432807dfab0dfb439a912577","last_reissued_at":"2026-05-18T00:40:18.745341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:18.745341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The size-Ramsey number of powers of paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Barnaby Roberts, Damian Reding, Dennis Clemens, Guilherme Oliveira Mota, Matthew Jenssen, Natasha Morrison, Yoshiharu Kohayakawa","submitted_at":"2017-07-13T20:14:06Z","abstract_excerpt":"Given graphs $G$ and $H$ and a positive integer $q$ say that $G$ is $q$-Ramsey for $H$, denoted $G\\rightarrow (H)_q$, if every $q$-colouring of the edges of $G$ contains a monochromatic copy of $H$. The size-Ramsey number $\\hat{r}(H)$ of a graph $H$ is defined to be $\\hat{r}(H)=\\min\\{|E(G)|\\colon G\\rightarrow (H)_2\\}$. Answering a question of Conlon, we prove that, for every fixed $k$, we have $\\hat{r}(P_n^k)=O(n)$, where $P_n^k$ is the $k$-th power of the $n$-vertex path $P_n$ (i.e. , the graph with vertex set $V(P_n)$ and all edges $\\{u,v\\}$ such that the distance between $u$ and $v$ in $P_n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04297","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.04297","created_at":"2026-05-18T00:40:18.745431+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.04297v1","created_at":"2026-05-18T00:40:18.745431+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04297","created_at":"2026-05-18T00:40:18.745431+00:00"},{"alias_kind":"pith_short_12","alias_value":"NRHMKCIYH4YA","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"NRHMKCIYH4YANMME","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"NRHMKCIY","created_at":"2026-05-18T12:31:34.259226+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NRHMKCIYH4YANMME2BLGDQJON3","json":"https://pith.science/pith/NRHMKCIYH4YANMME2BLGDQJON3.json","graph_json":"https://pith.science/api/pith-number/NRHMKCIYH4YANMME2BLGDQJON3/graph.json","events_json":"https://pith.science/api/pith-number/NRHMKCIYH4YANMME2BLGDQJON3/events.json","paper":"https://pith.science/paper/NRHMKCIY"},"agent_actions":{"view_html":"https://pith.science/pith/NRHMKCIYH4YANMME2BLGDQJON3","download_json":"https://pith.science/pith/NRHMKCIYH4YANMME2BLGDQJON3.json","view_paper":"https://pith.science/paper/NRHMKCIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.04297&json=true","fetch_graph":"https://pith.science/api/pith-number/NRHMKCIYH4YANMME2BLGDQJON3/graph.json","fetch_events":"https://pith.science/api/pith-number/NRHMKCIYH4YANMME2BLGDQJON3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NRHMKCIYH4YANMME2BLGDQJON3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NRHMKCIYH4YANMME2BLGDQJON3/action/storage_attestation","attest_author":"https://pith.science/pith/NRHMKCIYH4YANMME2BLGDQJON3/action/author_attestation","sign_citation":"https://pith.science/pith/NRHMKCIYH4YANMME2BLGDQJON3/action/citation_signature","submit_replication":"https://pith.science/pith/NRHMKCIYH4YANMME2BLGDQJON3/action/replication_record"}},"created_at":"2026-05-18T00:40:18.745431+00:00","updated_at":"2026-05-18T00:40:18.745431+00:00"}