{"paper":{"title":"Every plane graph of maximum degree 8 has an edge-face 9-colouring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jean-S\\'ebastien Sereni, Mat\\v{e}j Stehl\\'ik, Ross J. Kang","submitted_at":"2009-12-24T20:24:37Z","abstract_excerpt":"An edge-face colouring of a plane graph with edge set $E$ and face set $F$ is a colouring of the elements of $E \\cup F$ such that adjacent or incident elements receive different colours. Borodin proved that every plane graph of maximum degree $\\Delta\\ge10$ can be edge-face coloured with $\\Delta+1$ colours. Borodin's bound was recently extended to the case where $\\Delta=9$. In this paper, we extend it to the case $\\Delta=8$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.4770","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"}