{"paper":{"title":"Vertex-Coloring Edge-Weighting of Bipartite Graphs with Two Edge Weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongliang Lu","submitted_at":"2013-07-07T13:21:54Z","abstract_excerpt":"Let $G$ be a graph and $\\mathcal {S}$ be a subset of $Z$. A vertex-coloring $\\mathcal {S}$-edge-weighting of $G$ is an assignment of weight $s$ by the elements of $\\mathcal {S}$ to each edge of $G$ so that adjacent vertices have different sums of incident edges weights.\n  It was proved that every 3-connected bipartite graph admits a vertex-coloring $\\{1,2\\}$-edge-weighting (Lu, Yu and Zhang, (2011) \\cite{LYZ}). In this paper, we show that the following result: if a 3-edge-connected bipartite graph $G$ with minimum degree $\\delta$ contains a vertex $u\\in V(G)$ such that $d_G(u)=\\delta$ and $G-u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1863","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"}