{"paper":{"title":"On the precise value of the strong chromatic-index of a planar graph with a large girth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gerard Jennhwa Chang, Guan-Huei Duh","submitted_at":"2015-08-12T20:08:42Z","abstract_excerpt":"A strong $k$-edge-coloring of a graph $G$ is a mapping from $E(G)$ to $\\{1,2,\\ldots,k\\}$ such that every pair of distinct edges at distance at most two receive different colors. The strong chromatic index $\\chi'_s(G)$ of a graph $G$ is the minimum $k$ for which $G$ has a strong $k$-edge-coloring. Denote $\\sigma(G)=\\max_{xy\\in E(G)}\\{\\operatorname{deg}(x)+\\operatorname{deg}(y)-1\\}$. It is easy to see that $\\sigma(G) \\le \\chi'_s(G)$ for any graph $G$, and the equality holds when $G$ is a tree. For a planar graph $G$ of maximum degree $\\Delta$, it was proved that $\\chi'_s(G) \\le 4 \\Delta +4$ by u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03052","kind":"arxiv","version":3},"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"}