{"paper":{"title":"Some remarks on relations between the $\\mu$-parameters of regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"N.N. Davtyan, R.R. Kamalian","submitted_at":"2013-08-15T07:07:50Z","abstract_excerpt":"For an undirected, simple, finite, connected graph $G$, we denote by $V(G)$ and $E(G)$ the sets of its vertices and edges, respectively. A function $\\varphi:E(G)\\rightarrow \\{1,...,t\\}$ is called a proper edge $t$-coloring of a graph $G$, if adjacent edges are colored differently and each of $t$ colors is used. The least value of $t$ for which there exists a proper edge $t$-coloring of a graph $G$ is denoted by $\\chi'(G)$. For any graph $G$, and for any integer $t$ satisfying the inequality $\\chi'(G)\\leq t\\leq |E(G)|$, we denote by $\\alpha(G,t)$ the set of all proper edge $t$-colorings of $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3322","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"}