{"paper":{"title":"Universal Slope Sets for Upward Planar Drawings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Emilio Di Giacomo, Fabrizio Montecchiani, Giuseppe Liotta, Michael A. Bekos, Walter Didimo","submitted_at":"2018-03-27T08:12:19Z","abstract_excerpt":"We prove that every set $\\mathcal S$ of $\\Delta$ slopes containing the horizontal slope is universal for $1$-bend upward planar drawings of bitonic $st$-graphs with maximum vertex degree $\\Delta$, i.e., every such digraph admits a $1$-bend upward planar drawing whose edge segments use only slopes in $\\mathcal S$. This result is worst-case optimal in terms of the number of slopes, and, for a suitable choice of $\\mathcal S$, it gives rise to drawings with worst-case optimal angular resolution. In addition, we prove that every such set $\\mathcal S$ can be used to construct $2$-bend upward planar "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09949","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"}