{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,24]],"date-time":"2026-05-24T15:03:12Z","timestamp":1779634992566,"version":"3.53.1"},"reference-count":0,"publisher":"Journal of Graph Algorithms and Applications","issue":"2","license":[{"start":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T00:00:00Z","timestamp":1777334400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JGAA"],"abstract":"<jats:p>We study 3-plane drawings, that is, drawings of graphs in which every edge has at most three crossings. We show how the recently developed Density Formula for topological drawings of graphs [9] can be used to count the crossings in terms of the number n of vertices. As a main result, we show that every 3-plane drawing has at most 5.5(n \u2212 2) crossings, which is tight. In particular, it follows that every 3-planar graph on n vertices has crossing number at most 5.5n, which improves upon a recent bound [3] of 6.6n. To apply the Density Formula, we carefully analyze the interplay between certain configurations of cells in a 3-plane drawing. As a by-product, we also obtain an alternative proof for the known statement that every 3-planar graph has at most 5.5(n \u2212 2) edges.<\/jats:p>","DOI":"10.7155\/jgaa.v30i2.3117","type":"journal-article","created":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T14:01:06Z","timestamp":1777384866000},"page":"1-21","source":"Crossref","is-referenced-by-count":0,"title":["Crossing Number of Simple 3-Plane Drawings"],"prefix":"10.7155","volume":"30","author":[{"given":"Torsten","family":"Ueckerdt","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Miriam","family":"Goetze","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Hoffmann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3794-4406","authenticated-orcid":false,"given":"Ignaz","family":"Rutter","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"4175","published-online":{"date-parts":[[2026,4,28]]},"container-title":["Journal of Graph Algorithms and Applications"],"original-title":[],"link":[{"URL":"https:\/\/jgaa.info\/index.php\/jgaa\/article\/download\/3117\/3025","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/jgaa.info\/index.php\/jgaa\/article\/download\/3117\/3025","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,24]],"date-time":"2026-05-24T14:05:51Z","timestamp":1779631551000},"score":1,"resource":{"primary":{"URL":"https:\/\/jgaa.info\/index.php\/jgaa\/article\/view\/3117"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,28]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,4,28]]}},"URL":"https:\/\/doi.org\/10.7155\/jgaa.v30i2.3117","relation":{},"ISSN":["1526-1719"],"issn-type":[{"value":"1526-1719","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,28]]}}}