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Strong Hanani–Tutte on the Projective Plane

2009; Society for Industrial and Applied Mathematics; Volume: 23; Issue: 3 Linguagem: Inglês

10.1137/08072485x

1095-7146

Michael J. Pelsmajer, Marcus Schaefer, Despina Stasi,

Graph Theory and Algorithms

Previous article Next article Strong Hanani–Tutte on the Projective PlaneMichael J. Pelsmajer, Marcus Schaefer, and Despina StasiMichael J. Pelsmajer, Marcus Schaefer, and Despina Stasihttps://doi.org/10.1137/08072485XPDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractIf a graph can be drawn in the projective plane so that every two nonadjacent edges cross an even number of times, then the graph can be embedded in the projective plane.[1] D. Archdeacon, A Kuratowski theorem for the projective plane, J. Graph Theory, 5 (1981), pp. 243–246. JGTHDO 0364-9024 CrossrefISIGoogle Scholar[2] G. Cairns and and Y. Nikolayevsky, Bounds for generalized thrackles, Discrete Comput. Geom., 23 (2000), pp. 191–206. DCGEER 0179-5376 CrossrefISIGoogle Scholar[3] Google Scholar[4] H. H. Glover, , J. P. Huneke and , and C. S. Wang, $103$ graphs that are irreducible for the projective plane, J. Combin. Theory Ser. B, 27 (1979), pp. 332–370. JCBTB8 0095-8956 CrossrefISIGoogle Scholar[5] B. Mohar and and N. Robertson, Disjoint essential cycles, J. Combin. Theory Ser. B, 68 (1996), pp. 324–349. JCBTB8 0095-8956 CrossrefISIGoogle Scholar[6] Google Scholar[7] M. J. Pelsmajer, , M. Schaefer and , and D. Štefankovič, Removing even crossings, J. Combin. Theory Ser. B, 97 (2007), pp. 489–500. JCBTB8 0095-8956 CrossrefISIGoogle Scholar[8] Google Scholar[9] H. van der Holst, Algebraic characterizations of outerplanar and planar graphs, European J. Combin., 28 (2007), pp. 2156–2166. EJOCDI 0195-6698 CrossrefISIGoogle ScholarKeywordsHanani–Tutte theoremprojective planecrossing numberindependent odd crossing number Previous article Next article FiguresRelatedReferencesCited byDetails The $$\mathbb {Z}_2$$-Genus of Kuratowski Minors9 July 2022 | Discrete & Computational Geometry, Vol. 68, No. 2 Cross Ref Counterexample to an Extension of the Hanani-Tutte Theorem on the Surface of Genus 429 October 2019 | Combinatorica, Vol. 39, No. 6 Cross Ref A Direct Proof of the Strong Hanani–Tutte Theorem on the Projective Plane8 December 2016 Cross Ref Hanani-Tutte for Radial Planarity27 November 2015 Cross Ref Towards the Hanani-Tutte Theorem for Clustered Graphs21 October 2014 Cross Ref Clustered Planarity Testing Revisited Cross Ref Block Additivity of ℤ2-Embeddings Cross Ref Toward a Theory of Planarity: Hanani-Tutte and Planarity Variants Cross Ref Hanani-Tutte and Related Results Cross Ref Adjacent Crossings Do Matter Cross Ref Removing Independently Even CrossingsMichael J. Pelsmajer, Marcus Schaefer, and Daniel Štefankovič14 April 2010 | SIAM Journal on Discrete Mathematics, Vol. 24, No. 2AbstractPDF (225 KB)Removing Independently Even Crossings Cross Ref Removing even crossings on surfacesEuropean Journal of Combinatorics, Vol. 30, No. 7 Cross Ref Volume 23, Issue 3| 2009SIAM Journal on Discrete Mathematics History Submitted:21 May 2008Accepted:18 May 2009Published online:26 August 2009 InformationCopyright © 2009 Society for Industrial and Applied MathematicsKeywordsHanani–Tutte theoremprojective planecrossing numberindependent odd crossing numberMSC codes05C10PDF Download Article & Publication DataArticle DOI:10.1137/08072485XArticle page range:pp. 1317-1323ISSN (print):0895-4801ISSN (online):1095-7146Publisher:Society for Industrial and Applied Mathematics