{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T22:27:09Z","timestamp":1770071229131,"version":"3.49.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The geometric thickness of a graph $G$ is the minimum integer $k$ such that there is a straight line drawing of $G$ with its edge set partitioned into $k$ plane subgraphs. Eppstein [Separating thickness from geometric thickness. In Towards a Theory of Geometric Graphs, vol. 342 of Contemp. Math., AMS, 2004] asked whether every graph of bounded maximum degree has bounded geometric thickness. We answer this question in the negative, by proving that there exists $\\Delta$-regular graphs with arbitrarily large geometric thickness. In particular, for all $\\Delta\\geq9$ and for all large $n$, there exists a $\\Delta$-regular graph with geometric thickness at least $c\\sqrt{\\Delta}\\,n^{1\/2-4\/\\Delta-\\epsilon}$. Analogous results concerning graph drawings with few edge slopes are also presented, thus solving open problems by Dujmovi\u0107 et al. [Really straight graph drawings. In Proc. 12th International Symp. on Graph Drawing (GD '04), vol. 3383 of Lecture Notes in Comput. Sci., Springer, 2004] and Ambrus et al. [The slope parameter of graphs. Tech. Rep. MAT-2005-07, Department of Mathematics, Technical University of Denmark, 2005].<\/jats:p>","DOI":"10.37236\/1029","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:06:44Z","timestamp":1578701204000},"source":"Crossref","is-referenced-by-count":32,"title":["Bounded-Degree Graphs have Arbitrarily Large Geometric Thickness"],"prefix":"10.37236","volume":"13","author":[{"given":"J\u00e1nos","family":"Bar\u00e1t","sequence":"first","affiliation":[]},{"given":"Ji\u0159\u00ed","family":"Matou\u0161ek","sequence":"additional","affiliation":[]},{"given":"David R.","family":"Wood","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,1,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r3\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r3\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:26:56Z","timestamp":1579303616000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1029","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1,7]]},"article-number":"R3"}}