{"paper":{"title":"On-line coloring between two lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Piotr Micek, Stefan Felsner, Torsten Ueckerdt","submitted_at":"2014-11-03T09:12:21Z","abstract_excerpt":"We study on-line colorings of certain graphs given as intersection graphs of objects \"between two lines\", i.e., there is a pair of horizontal lines such that each object of the representation is a connected set contained in the strip between the lines and touches both. Some of the graph classes admitting such a representation are permutation graphs (segments), interval graphs (axis-aligned rectangles), trapezoid graphs (trapezoids) and cocomparability graphs (simple curves). We present an on-line algorithm coloring graphs given by convex sets between two lines that uses $O(\\omega^3)$ colors on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0402","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"}