{"paper":{"title":"Some bounds on the number of colors in interval and cyclic interval edge colorings of graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carl Johan Casselgren, Hrant H. Khachatrian, Petros A. Petrosyan","submitted_at":"2016-11-21T20:57:09Z","abstract_excerpt":"An \\emph{interval $t$-coloring} of a multigraph $G$ is a proper edge coloring with colors $1,\\dots,t$ such that the colors on the edges incident to every vertex of $G$ are colored by consecutive colors. A \\emph{cyclic interval $t$-coloring} of a multigraph $G$ is a proper edge coloring with colors $1,\\dots,t$ such that the colors on the edges incident to every vertex of $G$ are colored by consecutive colors, under the condition that color $1$ is considered as consecutive to color $t$. Denote by $w(G)$ ($w_{c}(G)$) and $W(G)$ ($W_{c}(G)$) the minimum and maximum number of colors in a (cyclic) i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07011","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"}