{"paper":{"title":"A note on the existence of an alternating sign on a spanning tree of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Dongseok Kim, Jaeun Lee, Young Soo Kwon","submitted_at":"2011-06-03T10:27:23Z","abstract_excerpt":"For a spanning tree T of a connected graph G and for a labelling \\phi: E(T) \\rightarrow {+, -}, \\phi is called an alternating sign on a spanning tree T of a graph G if for any cotree edge e \\in E(G)-E(T), the unique path in T joining both end vertices of e has alternating signs. In the present note, we prove that any graph has a spanning tree T and an alternating sign on T."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0605","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"}