{"paper":{"title":"Distinguishing Chromatic Number of Random Cayley graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Niranjan Balachandran, Sajith Padinhatteeri","submitted_at":"2014-06-20T11:53:15Z","abstract_excerpt":"The \\textit{Distinguishing Chromatic Number} of a graph $G$, denoted $\\chi_D(G)$, was first defined in \\cite{collins} as the minimum number of colors needed to properly color $G$ such that no non-trivial automorphism $\\phi$ of the graph $G$ fixes each color class of $G$. In this paper, we consider random Cayley graphs $\\Gamma(A,S)$ defined over certain abelian groups $A$ and show that with probability at least $1-n^{-\\Omega(\\log n)}$ we have, $\\chi_D(\\Gamma)\\le\\chi(\\Gamma) + 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5358","kind":"arxiv","version":3},"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"}