{"paper":{"title":"On Sierpi\\'{n}ski packing chromatic number and recognition of Sierpi\\'{n}ski products","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"P\\v{r}emysl Holub, Sandi Klav\\v{z}ar","submitted_at":"2025-07-09T10:43:11Z","abstract_excerpt":"The Sierpi\\'{n}ski product $G \\otimes _f H$ of graphs $G$ and $H$ with respect to a function $f \\colon V(G)\\rightarrow V(H)$ has the vertex set $V(G)\\times V(H)$. For every $g\\in V(G)$ it contains a disjoint copy $gH$ of $H$, and for every edge $gg'$ of $G$ there is the edge $(g,f(g'))(g',f(g))$ between $gH$ and $g'H$. In this paper, the Sierpi\\'{n}ski packing chromatic number is defined as the minimum of $\\chi_{\\rho}(G\\otimes _f H)$ over all functions $f$, where $\\chi_{\\rho}(X)$ is the packing chromatic number of $X$. The upper Sierpi\\'{n}ski packing chromatic number is analogously defined as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06730","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/2507.06730/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"}