{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:07:19Z","timestamp":1758823639242},"reference-count":3,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2006,10]]},"abstract":"<jats:p>Let G be a graph of n vertices with maximum degree d that can be drawn without crossing in a closed surface of Euler characteristic \u03c7. It is proved that then G can be drawn in the plane with at most c<jats:sub>\u03c7<\/jats:sub>dn crossings, where c<jats:sub>\u03c7<\/jats:sub>is a constant depending only on \u03c7. This result, which is tight up to a constant factor, is strengthened and generalized to the case when there is no restriction on the degrees of the vertices.<\/jats:p>","DOI":"10.1142\/s0129054106004236","type":"journal-article","created":{"date-parts":[[2006,9,18]],"date-time":"2006-09-18T12:04:43Z","timestamp":1158581083000},"page":"1005-1015","source":"Crossref","is-referenced-by-count":9,"title":["PLANAR CROSSING NUMBERS OF GRAPHS EMBEDDABLE IN ANOTHER SURFACE"],"prefix":"10.1142","volume":"17","author":[{"given":"K\u00c1ROLY J.","family":"B\u00d6R\u00d6ZKY","sequence":"first","affiliation":[{"name":"R\u00e9nyi Institute, Hungarian Academy of Sciences, Hungary"}]},{"given":"J\u00c1NOS","family":"PACH","sequence":"additional","affiliation":[{"name":"R\u00e9nyi Institute, Hungarian Academy of Sciences, Hungary"}]},{"given":"G\u00c9ZA","family":"T\u00d3TH","sequence":"additional","affiliation":[{"name":"R\u00e9nyi Institute, Hungarian Academy of Sciences, Hungary"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf2","volume-title":"Algebraic topology","author":"Hatcher A.","year":"2002"},{"key":"rf3","series-title":"Johns Hopkins Studies in the Mathematical Sciences","doi-asserted-by":"crossref","DOI":"10.56021\/9780801866890","volume-title":"Graphs on surfaces","author":"Mohar B.","year":"2001"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/11618058_30"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054106004236","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,6]],"date-time":"2024-02-06T13:51:23Z","timestamp":1707227483000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054106004236"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,10]]},"references-count":3,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,10]]}},"alternative-id":["10.1142\/S0129054106004236"],"URL":"https:\/\/doi.org\/10.1142\/s0129054106004236","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,10]]}}}