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Blocking nonorientability of a surface

Bojan Mohar, Alexander Schrijver
<span title="">2003</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g6u5fful5vcr3a7gppc6y47el4" style="color: black;">Journal of combinatorial theory. Series B (Print)</a> </i> &nbsp;
Let S be a nonorientable surface. A collection of pairwise noncrossing simple closed curves in S is a blockage if every onesided simple closed curve in S crosses at least one of them.  ...  Robertson and Thomas [9] conjectured that the orientable genus of any graph G embedded in S with sufficiently large face-width is "roughly" equal to one half of the minimum number of intersections of a  ...  The orientable genus of graphs with a given nonorientable embedding Let Π be a (2-cell) embedding of a graph G into a nonplanar surface S, i.e. a surface distinct from the 2-sphere.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0095-8956(02)00025-4">doi:10.1016/s0095-8956(02)00025-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/44okpg3d6jb3ncbzo6lkekvv6m">fatcat:44okpg3d6jb3ncbzo6lkekvv6m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809104014/http://www.fmf.uni-lj.si/~mohar/Reprints/2003/BM03_JCT87_Schrijver_BlockingNonorientability.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/58/9c/589c3e9846078a79b31c5d4411fa91fde2d0087f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0095-8956(02)00025-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Lyapunov graphs and flows on surfaces

K. A. de Rezende, R. D. Franzosa
<span title="1993-02-01">1993</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/w3g32txdvneltemssag5nwfxcy" style="color: black;">Transactions of the American Mathematical Society</a> </i> &nbsp;
In this paper, a characterization of Lyapunov graphs associated to smooth flows on surfaces is presented.  ...  Moreover, an algorithmic geometric construction of flows on surfaces is described.  ...  By a nonorientable basic set we mean a basic set with a nonorientable basic block yVA e, and by a nonorientable vertex in a Lyapunov graph we mean a vertex associated to a nonorientable basic set.  ... 
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The page number of genus g graphs is (g)

L. Heath, S. Istrail
<span title="">1987</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jlc5kugafjg4dl7ozagimqfcbm" style="color: black;">Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC &#39;87</a> </i> &nbsp;
Separate book embedding algorithms are given for the cases of graphs embedded m orlentable and nonorientable surfaces.  ...  An important aspect of the construction is a new decomposition theorem, of independent interest, for a graph embedded on a surface.  ...  We also thank the referees for a careful reading, for many helpful comments, for sharpening the proof of Lemma 2, and for improving the discussion of the algorithm N-LAYOUT.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/28395.28437">doi:10.1145/28395.28437</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/stoc/HeathI87.html">dblp:conf/stoc/HeathI87</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gkamzdrdlzei5bnflrsn3nlwum">fatcat:gkamzdrdlzei5bnflrsn3nlwum</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20120910051405/http://www.cs.brown.edu/~sorin/pdfs/the%20pagenumber%20of%20genus%20g%20graphs%20is%20o.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/16/00/160054152a26769f82ea3ac90063cef131b30c13.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/28395.28437"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

The pagenumber of genus g graphs is O(g)

Lenwood S. Heath, Sorin Istrail
<span title="1992-07-01">1992</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/r72grtxx6jad5hjzl7fxcunwhi" style="color: black;">Journal of the ACM</a> </i> &nbsp;
Separate book embedding algorithms are given for the cases of graphs embedded m orlentable and nonorientable surfaces.  ...  An important aspect of the construction is a new decomposition theorem, of independent interest, for a graph embedded on a surface.  ...  We also thank the referees for a careful reading, for many helpful comments, for sharpening the proof of Lemma 2, and for improving the discussion of the algorithm N-LAYOUT.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/146637.146643">doi:10.1145/146637.146643</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hlgzjpndfjfqxomekkalifuc3u">fatcat:hlgzjpndfjfqxomekkalifuc3u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20120910051405/http://www.cs.brown.edu/~sorin/pdfs/the%20pagenumber%20of%20genus%20g%20graphs%20is%20o.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/16/00/160054152a26769f82ea3ac90063cef131b30c13.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/146637.146643"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Self-dual embeddings of complete bipartite graphs

Dan Archdeacon, Nora Hartsfield
<span title="">1992</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g6u5fful5vcr3a7gppc6y47el4" style="color: black;">Journal of combinatorial theory. Series B (Print)</a> </i> &nbsp;
In this paper we examine self-dual embeddings of the complete bipartite graph K", on both orientable and nonorientable surfaces.  ...  We show by construction that these necessary conditions are sufficient, except that there is no orientable self-dual embedding of K6,6. 0  ...  ACKNOWLEDGMENT The authors thank Richard Wilson for the embedding of Kp dual to K6,6  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0095-8956(92)90056-4">doi:10.1016/0095-8956(92)90056-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6mnkxinrejhgrcc3gys4z3ja64">fatcat:6mnkxinrejhgrcc3gys4z3ja64</a> </span>
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Contents

<span title="">2004</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
Ota Chromatic numbers and cycle parities of quadrangulations on nonorientable closed surfaces 211 M.I. Ostrovskii Minimal congestion trees 219 C. Peters and L.  ...  Levy Injectivity and surjectivity of Collatz functions 191 E.G. Mphako H-lifts of tangential k-blocks 201 A. Nakamoto, S. Negami and K.  ...  Winzen Almost regular multipartite tournaments containing a Hamiltonian path through a given arc 267  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0012-365x(04)00280-8">doi:10.1016/s0012-365x(04)00280-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gv6egom3pffcjhh2yfx5bvnycq">fatcat:gv6egom3pffcjhh2yfx5bvnycq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190321210102/https://core.ac.uk/download/pdf/82517298.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/77/d4/77d448a3362db7630ed94adabb60f148b954276c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0012-365x(04)00280-8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Matroids Determine the Embeddability of Graphs in Surfaces

Thomas Zaslavsky
<span title="">1989</span> <i title="JSTOR"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/a64sw4kcsveajhudnssdwrwvze" style="color: black;">Proceedings of the American Mathematical Society</a> </i> &nbsp;
An embedding of a finite graph T in a surface S is a homeomorphism of Y, regarded as a topological space, with a closed subset of S.  ...  The embeddability of a graph in a given surface is determined entirely by the polygon matroid of the graph.  ...  d(r) = min{2g(r),h(T)}, the smallest demigenus of a compact surface in which T embeds.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2047303">doi:10.2307/2047303</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qyzwvrn7wbd6pghlzuw24mgrdm">fatcat:qyzwvrn7wbd6pghlzuw24mgrdm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170820144959/http://www.ams.org/journals/proc/1989-106-04/S0002-9939-1989-0979055-7/S0002-9939-1989-0979055-7.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b4/f6/b4f6aed7a082c94a9d1050dcc10b5260dbf73037.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2047303"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> jstor.org </button> </a>

Matroids determine the embeddability of graphs in surfaces

Thomas Zaslavsky
<span title="1989-04-01">1989</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/a64sw4kcsveajhudnssdwrwvze" style="color: black;">Proceedings of the American Mathematical Society</a> </i> &nbsp;
An embedding of a finite graph T in a surface S is a homeomorphism of Y, regarded as a topological space, with a closed subset of S.  ...  The embeddability of a graph in a given surface is determined entirely by the polygon matroid of the graph.  ...  d(r) = min{2g(r),h(T)}, the smallest demigenus of a compact surface in which T embeds.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9939-1989-0979055-7">doi:10.1090/s0002-9939-1989-0979055-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/x3vqicuu7jeo5iajv5oiipfi5i">fatcat:x3vqicuu7jeo5iajv5oiipfi5i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190503174606/https://www.ams.org/journals/proc/1989-106-04/S0002-9939-1989-0979055-7/S0002-9939-1989-0979055-7.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/35/71/357134fc65f6669a102869dc88f182fac4e85351.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9939-1989-0979055-7"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Book announcements

<span title="">1990</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
Representing surfaces by polygons. Pseudosurfaces and block designs. Orientations. Stars, links, and local properties).  ...  Nonorientable case 5. About nonorientable cases 11, 8, and 2). Chapter 6: The Genus of a Group. The genus of abelian groups (Recovering a Cayley graph from any of its quotients.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0166-218x(90)90074-m">doi:10.1016/0166-218x(90)90074-m</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uhwd4fl3wvcetkvers2zklsbry">fatcat:uhwd4fl3wvcetkvers2zklsbry</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190325122410/https://core.ac.uk/download/pdf/82077467.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7b/5a/7b5ac75a2603b8f53bccb88346c6ecd48a8e4bb9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0166-218x(90)90074-m"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Maximum genus embeddings of Steiner triple systems

Mike J. Grannell, Terry S. Griggs, Jozef Širáň
<span title="">2005</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/54t3hgai4fhhthc74mj7z7tapu" style="color: black;">European journal of combinatorics (Print)</a> </i> &nbsp;
We prove that for n > 3 every STS(n) has both an orientable and a nonorientable embedding in which the triples of the STS(n) appear as triangular faces and there is just one additional large face.  ...  We also obtain detailed results about the possible automorphisms of such embeddings.  ...  Such a biembedding comprises a face 2-colourable triangulation of a complete graph K n in an orientable or in a nonorientable surface S.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ejc.2004.01.014">doi:10.1016/j.ejc.2004.01.014</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i3rp3awda5dr7feyqo4kzljea4">fatcat:i3rp3awda5dr7feyqo4kzljea4</a> </span>
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Page 4226 of Mathematical Reviews Vol. , Issue 96g [page]

<span title="">1996</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The second idea of the construction is the use, as the mentioned block groups G;, of some special finitely generated groups isomorphic to surface bundle groups.  ...  When both are nonorientable, there are two further conditions. Finally, periodic homeomorphisms of nonorientable surfaces having odd order can be classified by lifting to the orientable double cover.  ... 
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Knots and nonorientable surfaces in chiral nematics

T. Machon, G. P. Alexander
<span title="2013-08-12">2013</span> <i title="Proceedings of the National Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nvtuoas5pbdsllkntnhizy4f4q" style="color: black;">Proceedings of the National Academy of Sciences of the United States of America</a> </i> &nbsp;
Extending this existing work, we describe the full topological implications of colloids representing non-orientable surfaces and use it to construct torus knots and links of type (p,2) around multiply-twisted  ...  Knots and knotted fields enrich physical phenomena ranging from DNA and molecular chemistry to the vortices of fluid flows and textures of ordered media.  ...  This work was also supported by a University of Warwick Chancellor's International Scholarship (to T.M.).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1073/pnas.1308225110">doi:10.1073/pnas.1308225110</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/23940365">pmid:23940365</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC3761586/">pmcid:PMC3761586</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2mhzuteftzbhhgfk3gkm3qolvq">fatcat:2mhzuteftzbhhgfk3gkm3qolvq</a> </span>
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Classification of nonorientable regular embeddings of Hamming graphs

Gareth A. Jones, Young Soo Kwon
<span title="">2012</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/54t3hgai4fhhthc74mj7z7tapu" style="color: black;">European journal of combinatorics (Print)</a> </i> &nbsp;
By a regular embedding of a graph K in a surface we mean a 2-cell embedding of K in a compact connected surface such that the automorphism group acts regularly on flags.  ...  In this paper, we classify the nonorientable regular embeddings of the Hamming graph H(d, n).  ...  K 6 in the real projective plane and in a nonorientable surface of genus 5.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ejc.2012.04.001">doi:10.1016/j.ejc.2012.04.001</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/h7dzox4egvcm5fxdflu4bv3nam">fatcat:h7dzox4egvcm5fxdflu4bv3nam</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170926023512/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/354/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDE5NTY2OTgxMjAwMDc0MQ%3D%3D.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f7/28/f7282d8049408848caf0c1fb08aee13f170de934.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ejc.2012.04.001"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

On the orientable genus of graphs with bounded nonorientable genus

Bojan Mohar
<span title="">1998</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
A conjecture of Robertson and Thomas on the orientable genus of graphs with a given nonorientable embedding is disproved.  ...  least one of the curves 7tl ..... 7p, then we say that the family F is a blockage and that F blocks 1-sided curves in the surface.  ...  If Z is a surface, we denote by 9(27) its genus (or the nonorientable genus if Z is nonorientable).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0012-365x(97)00144-1">doi:10.1016/s0012-365x(97)00144-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fuldkpvqivby3n6sgnvbnnxbqq">fatcat:fuldkpvqivby3n6sgnvbnnxbqq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829065816/https://www.fmf.uni-lj.si/~mohar/Reprints/1998/BM98_DM182_Mohar_OrientableGenus.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c7/12/c7120cf827c1b417a1553fae86615720a8006249.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0012-365x(97)00144-1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Classification of nonorientable regular embeddings of Hamming graphs [article]

Gareth A. Jones, Young Soo Kwon
<span title="2011-07-16">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
By a regular embedding of a graph K in a surface we mean a 2-cell embedding of K in a compact connected surface such that the automorphism group acts regularly on flags.  ...  In this paper, we classify the nonorientable regular embeddings of the Hamming graph H(d,n).  ...  K 6 in the real projective plane and in a nonorientable surface of genus 5.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1107.3187v1">arXiv:1107.3187v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/43byhegwxngypkdvkhv46o7j4y">fatcat:43byhegwxngypkdvkhv46o7j4y</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1107.3187/1107.3187.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1107.3187v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>
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