{"paper":{"title":"On the character degree graph of solvable groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Carlo Casolo, Emanuele Pacifici, Khatoon Khedri, Silvio Dolfi, Zeinab Akhlaghi","submitted_at":"2017-06-14T07:58:52Z","abstract_excerpt":"Let \\(G\\) be a finite solvable group, and let \\(\\Delta(G)\\) denote the \\emph{prime graph} built on the set of degrees of the irreducible complex characters of \\(G\\). A fundamental result by P.P. P\\'alfy asserts that the complement $\\bar{\\Delta}(G)$ of the graph \\(\\Delta(G)\\) does not contain any cycle of length \\(3\\). In this paper we generalize P\\'alfy's result, showing that $\\bar{\\Delta}(G)$ does not contain any cycle of odd length, whence it is a bipartite graph. As an immediate consequence, the set of vertices of \\(\\Delta(G)\\) can be covered by two subsets, each inducing a complete subgrap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04351","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":""},"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"}