{"paper":{"title":"On the distinguishing chromatic number in hereditary graph classes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christoph Brause, Ingo Schiemeyer, Monika Pil\\'sniak, Rafa{\\l} Kalinowski","submitted_at":"2025-05-22T18:03:55Z","abstract_excerpt":"The distinguishing chromatic number of a graph $G$, denoted $\\chi_D(G)$, is the minimum number of colours in a proper vertex colouring of $G$ that is preserved by the identity automorphism only. Collins and Trenk proved that $\\chi_D(G)\\le 2\\Delta(G)$ for any connected graph $G$, and the equality holds for complete balanced bipartite graphs $K_{p,p}$ and for $C_6$. In this paper, we show that the upper bound on $\\chi_D(G)$ can be substantially reduced if we forbid some small graphs as induced subgraphs of $G$, that is, we study the distinguishing chromatic number in some hereditary graph classe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.17193","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/2505.17193/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"}