{"paper":{"title":"On the pseudoachromatic index of the complete graph III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C. Rubio-Montiel, G. Araujo-Pardo, J.J. Montellano-Ballesteros, R. Strausz","submitted_at":"2015-07-29T22:45:59Z","abstract_excerpt":"Let $ \\Pi_q $ be the projective plane of order $ q $, let $\\psi(m):=\\psi(L(K_m))$ the pseudoachromatic number of the complete line graph of order $ m $, let $ a\\in \\{ 3,4,\\dots,\\tfrac{q}{2}+1 \\} $ and $ m_a=(q+1)^2-a $.\n  In this paper, we improve the upper bound of $ \\psi(m) $ given by Araujo-Pardo et al. [J Graph Theory 66 (2011), 89--97] and Jamison [Discrete Math. 74 (1989), 99--115] in the following values: if $ x\\geq 2 $ is an integer and $m\\in \\{4x^2-x,\\dots,4x^2+3x-3\\}$ then $\\psi(m) \\leq 2x(m-x-1)$.\n  On the other hand, if $ q $ is even and there exists $ \\Pi_q $ we give a complete ed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08338","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"}