{"paper":{"title":"List Supermodular Coloring with Shorter Lists","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yu Yokoi","submitted_at":"2017-07-18T00:08:26Z","abstract_excerpt":"In 1995, Galvin proved that a bipartite graph $G$ admits a list edge coloring if every edge is assigned a color list of length $\\Delta(G)$, the maximum degree of the graph. This result was improved by Borodin, Kostochka and Woodall, who proved that $G$ still admits a list edge coloring if every edge $e=st$ is assigned a list of $\\max\\{d_{G}(s), d_{G}(t)\\}$ colors. Recently, Iwata and Yokoi provided the list supermodular coloring theorem, that extends Galvin's result to the setting of Schrijver's supermodular coloring. This paper provides a common generalization of these two extensions of Galvi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05417","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"}