{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:53Z","timestamp":1753893833984,"version":"3.41.2"},"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>We extend known results regarding the maximum rectilinear crossing number of the cycle graph ($C_n$) and the complete graph ($K_n$) to the class of general $d$-regular graphs $R_{n,d}$. We present the generalized star drawings of the $d$-regular graphs $S_{n,d}$ of order $n$ where $n+d\\equiv 1 \\pmod 2 $ and prove that they maximize the maximum rectilinear crossing numbers. A star-like drawing of $S_{n,d}$ for $n \\equiv d \\equiv 0 \\pmod 2$ is introduced and we conjecture that this drawing maximizes the maximum rectilinear crossing numbers, too. We offer a simpler proof of two results initially proved by Furry and Kleitman as partial results in the direction of this conjecture.<\/jats:p>","DOI":"10.37236\/143","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:32:02Z","timestamp":1578717122000},"source":"Crossref","is-referenced-by-count":2,"title":["The Maximum of the Maximum Rectilinear Crossing Numbers of $d$-Regular Graphs of Order $n$"],"prefix":"10.37236","volume":"16","author":[{"given":"Matthew","family":"Alpert","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elie","family":"Feder","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Heiko","family":"Harborth","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2009,4,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r54\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r54\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:55:47Z","timestamp":1579316147000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r54"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/143","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,4,30]]},"article-number":"R54"}}