{"paper":{"title":"Connected size Ramsey numbers of matchings versus a small path or cycle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ruyu Song, Sha Wang, Yanbo Zhang, Yixin Zhang","submitted_at":"2022-05-08T22:48:00Z","abstract_excerpt":"Given two graphs $G_1, G_2$, the connected size Ramsey number ${\\hat{r}}_c(G_1,G_2)$ is defined to be the minimum number of edges of a connected graph $G$, such that for any red-blue edge colouring of $G$, there is either a red copy of $G_1$ or a blue copy of $G_2$. Concentrating on ${\\hat{r}}_c(nK_2,G_2)$ where $nK_2$ is a matching, we generalise and improve two previous results as follows. Vito, Nabila, Safitri, and Silaban obtained the exact values of ${\\hat{r}}_c(nK_2,P_3)$ for $n=2,3,4$. We determine its exact values for all positive integers $n$. Rahadjeng, Baskoro, and Assiyatun proved "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.03965","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.03965/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}