{"paper":{"title":"$S_{12}$ and $P_{12}$-colorings of cubic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Anush Hakobyan, Vahan Mkrtchyan","submitted_at":"2018-07-21T12:29:27Z","abstract_excerpt":"If $G$ and $H$ are two cubic graphs, then an $H$-coloring of $G$ is a proper edge-coloring $f$ with edges of $H$, such that for each vertex $x$ of $G$, there is a vertex $y$ of $H$ with $f(\\partial_G(x))=\\partial_H(y)$. If $G$ admits an $H$-coloring, then we will write $H\\prec G$. The Petersen coloring conjecture of Jaeger ($P_{10}$-conjecture) states that for any bridgeless cubic graph $G$, one has: $P_{10}\\prec G$. The Sylvester coloring conjecture ($S_{10}$-conjecture) states that for any cubic graph $G$, $S_{10}\\prec G$. In this paper, we introduce two new conjectures that are related to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08138","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"}