{"paper":{"title":"Classification and Construction of Planar, 3-Connected Kronecker Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Riccardo W. Maffucci","submitted_at":"2024-02-02T13:41:31Z","abstract_excerpt":"We give a complete classification of the Kronecker (i.e. direct) product graphs that are planar and $3$-connected (i.e. $3$-polytopal). They are all of the form \\[H\\wedge K_2,\\] where $H$ is a $2$-connected graph, possibly non-planar, and satisfying specific properties that we will describe.\n  Our proof is constructive, in the sense that we prescribe how to obtain all such graphs $H$, by adding a few edges in a specific way to a given planar, bipartite graph, that is either $3$-connected, or semi-hyper-$2$-connected.\n  Moreover, for $H$ planar, we also give a more precise characterisation of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.01407","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/2402.01407/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"}