{"paper":{"title":"Harmonious Colorings: bounds, heuristics and integer-linear formulations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Beatriz Martins, J\\'ulio Ara\\'ujo, Manoel Camp\\^elo, Marcio C. Santos","submitted_at":"2026-05-18T16:42:24Z","abstract_excerpt":"A proper coloring $c$ of a simple graph $G$ is harmonious if, for every pair of distinct edges $uv,xy\\in E(G)$, we have that $\\{c(u),c(v)\\}\\neq \\{c(x),c(y)\\}$. The harmonious chromatic number of $G$, denoted by $h(G)$, is the least positive integer $k$ such that $G$ has a harmonious coloring with $k$ colors. In this work, we extend an idea presented in [Kolay, et al. Harmonious coloring: Parameterized algorithms and upper bounds. Theor. Comp. Sci. 772 (2019), 132-142] to compare the harmonious chromatic numbers of two graphs $G$ and $H$, with $H$ being obtained from $G$ by identifying vertices"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18634","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/2605.18634/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T00:01:59.198620Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"73ad2342962516d140c2ade07ec6eec9aee950b8fb882894f7e8fee1c23c6841"},"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"}