{"paper":{"title":"Injective Edge Chromatic Index of a Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Charles Dominic, Domingos M. Cardoso, J. Orestes Cerdeira, J. Pedro Cruz","submitted_at":"2015-10-09T10:54:21Z","abstract_excerpt":"Three edges $e_{1}, e_{2}$ and $e_{3}$ in a graph $G$ are consecutive if they form a path (in this order) or a cycle of length three. An injective edge coloring of a graph $G = (V,E)$ is a coloring $c$ of the edges of $G$ such that if $e_{1}, e_{2}$ and $e_{3}$ are consecutive edges in $G$, then $c(e_{1})\\neq c(e_3)$. The injective edge coloring number $\\chi_{i}^{'}(G)$ is the minimum number of colors permitted in such a coloring. In this paper, exact values of $\\chi_{i}^{'}(G)$ for several classes of graphs are obtained, upper and lower bounds for $\\chi_{i}^{'}(G)$ are introduced and it is pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02626","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"}