{"paper":{"title":"Shifts of the Stable Kneser Graphs and Hom-Idempotence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mario Valencia-Pabon, Pablo Torres","submitted_at":"2016-04-24T13:00:12Z","abstract_excerpt":"A graph $G$ is said to be {\\em hom-idempotent} if there is a homomorphism from $G^2$ to $G$, and {\\em weakly hom-idempotent} if for some $n \\geq 1$ there is a homomorphism from $G^{n+1}$ to $G^n$. Larose et al. [{\\em Eur. J. Comb. 19:867-881, 1998}] proved that Kneser graphs $\\operatorname{KG}(n,k)$ are not weakly hom-idempotent for $n \\geq 2k+1$, $k\\geq 2$. For $s \\geq 2$, we characterize all the shifts (i.e., automorphisms of the graph that map every vertex to one of its neighbors) of $s$-stable Kneser graphs $\\operatorname{KG}(n,k)_{s-\\operatorname{stab}}$ and we show that $2$-stable Kneser"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07023","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"}