{"paper":{"title":"On $\\omega \\psi$-Perfect Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C. Rubio-Montiel, G. Araujo-Pardo","submitted_at":"2015-07-24T16:54:17Z","abstract_excerpt":"In this paper, we generalize the concept of {\\it{perfect graphs}} to other parameters related to graph vertex coloring. This idea was introduced by Christen and Selkow in 1979 and Yegnanarayanan in 2001. Let $ a,b \\in \\{ \\omega, \\chi, \\Gamma, \\alpha, \\psi \\} $ where $ \\omega $ is the clique number, $ \\chi $ is the chromatic number, $ \\Gamma $ is the Grundy number, $ \\alpha $ is the achromatic number and $ \\psi $ is the pseudoachromatic number. A graph $ G $ is \\emph{$ ab $-perfect}, if for every induced subgraph $ H $ of $G$, $ a(H)$ equals $b(H) $. In this paper, we characterize the $ab$-perf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06919","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":""},"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"}