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 A110507 Number of nodes in the smallest cubic graph with crossing number n. 1
 4, 6, 10, 14, 16, 18, 20, 22, 24, 26, 26, 28 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The Coxeter graph on 28 vertices needs 11 crossings and the Levi graph on 30 requires 13. Haythorpe and Newcombe prove that a(11) > 26 and thus that a(11) = 28. - Jeremy Tan, Apr 30 2018 LINKS A. E. Brouwer, The Heawood Graph Geoff Exoo, Rectlinear Drawings of Famous Graphs Michael Haythorpe and Alex Newcombe, There are no Cubic Graphs on 26 Vertices with Crossing Number 11, arXiv preprint arXiv:1804.10336 [math.CO], 2018. Ed Pegg, Jr., Cubic Symmetric Graphs Ed Pegg, Jr., Cubic Symmetric Graphs Eric Weisstein, Graph Crossing Number EXAMPLE a(0) = 4 from the complete graph K_4. a(1) = 6 from the utility graph K_{3,3}. a(2) = 10 from the Petersen graph (and 1 other). a(3) = 14 from the Heawood graph (and 7 others). a(4) = 16 from the Moebius-Kantor graph (and 1 other). a(5) = 18 from the Pappus graph (and 1 other). a(6) = 20 from the Desargues graph (and 2 others based on 10_3 configurations). a(7) = 22 from the 7-crossing graphs (4 in total). a(8) = 24 from the McGee graph (and 3 others). a(9) = a(10) = 26 from the McGee graph + edge (and unknown others). a(11) = 28 from the Coxeter graph (and unknown others). CROSSREFS Sequence in context: A065073 A084997 A175706 * A224467 A134624 A171945 Adjacent sequences:  A110504 A110505 A110506 * A110508 A110509 A110510 KEYWORD nonn,more AUTHOR N. J. A. Sloane, based on email from Ed Pegg Jr, Mar 14 2007, Mar 16 2007, Jan 28 2009 EXTENSIONS a(11) added and offset corrected by Jeremy Tan, Apr 30 2018 STATUS approved

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Last modified May 27 21:20 EDT 2018. Contains 304726 sequences. (Running on oeis4.)