{"paper":{"title":"The Chromatic Number of Ordered Graphs With Constrained Conflict Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jonathan Rollin, Maria Axenovich, Torsten Ueckerdt","submitted_at":"2016-10-04T18:01:22Z","abstract_excerpt":"An ordered graph $G$ is a graph whose vertex set is a subset of integers. The edges are interpreted as tuples $(u,v)$ with $u < v$. For a positive integer $s$, a matrix $M \\in \\mathbb{Z}^{s \\times 4}$, and a vector $\\mathbf{p} = (p,\\ldots,p) \\in \\mathbb{Z}^s$ we build a conflict graph by saying that edges $(u,v)$ and $(x,y)$ are conflicting if $M(u,v,x,y)^\\top \\geq \\mathbf{p}$ or $M(x,y,u,v)^\\top \\geq \\mathbf{p}$, where the comparison is componentwise. This new framework generalizes many natural concepts of ordered and unordered graphs, such as the page-number, queue-number, band-width, interv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01111","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"}