{"paper":{"title":"Lit-only sigma-game on nondegenerate graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hau-wen Huang","submitted_at":"2012-09-06T09:16:53Z","abstract_excerpt":"A configuration of the lit-only $\\sigma$-game on a graph $\\Gamma$ is an assignment of one of two states, {\\it on} or {\\it off}, to each vertex of $\\Gamma.$ Given a configuration, a move of the lit-only $\\sigma$-game on $\\Gamma$ allows the player to choose an {\\it on} vertex $s$ of $\\Gamma$ and change the states of all neighbors of $s.$ Given an integer $k$, the underlying graph $\\Gamma$ is said to be $k$-lit if for any configuration, the number of {\\it on} vertices can be reduced to at most $k$ by a finite sequence of moves. We give a description of the orbits of the lit-only $\\sigma$-game on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1233","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"}