{"paper":{"title":"Semistrong edge coloring and $(0,1)$-relaxed strong edge coloring of graphs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Wensong Lin, Yuquan Lin","submitted_at":"2023-10-19T08:00:32Z","abstract_excerpt":"In this work, we study two relaxations of the well-known strong edge coloring.\n  A semistrong edge coloring of a graph G is an edge coloring in which every color class forms a matching M such that every edge of M is incident with at least one vertex of degree 1 in the subgraph of G induced by the vertices covered by M.\n  For any two nonnegative integers s and t, an (s,t)-relaxed strong edge coloring of G is an edge coloring in which, for every edge e of G, at most s edges at distance 1 and at most t edges at distance 2 from e receive the same color as e. The corresponding chromatic indices are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.12552","kind":"arxiv","version":2},"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/2310.12552/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"}