{"paper":{"title":"A note on a conjecture of star chromatic index for outerplanar graphs","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Qingye Yao, Xingchao Deng, Xudong Cui, Yanbing Zhang","submitted_at":"2020-06-01T02:42:19Z","abstract_excerpt":"A star edge coloring of a graph $G$ is a proper edge coloring of $G$ without bichromatic paths or cycles of length four. The it star chromatic index, $\\chi_{st}^{'} (G ),$ of $G$ is the minimum number $k$ for which $G$ has a star edge coloring by $k$ colors. In \\cite{LB},\n  L. Bezegov$\\acute{a}$ et al. conjectured that $\\chi_{st}^{'} (G )\\leq \\lfloor\\frac{3\\Delta}{2}\\rfloor+1$ when $G$ is an outerplanar graph with\n  maximum degree $\\Delta \\geq 3.$ In this paper we obtained that $\\chi_{st}^{'}(G) \\leq \\Delta+6$ when $G$ is an 2-connected outerplanar graph with diameter 2 or 3. If $G$ is an 2-co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.00675","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.00675/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}