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Blocking nonorientability of a surface
<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>
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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. ...
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Lyapunov graphs and flows on surfaces
<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>
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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)
<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 '87</a>
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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. ...
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The pagenumber of genus g graphs is O(g)
<span title="1992-07-01">1992</span>
<i title="Association for Computing Machinery (ACM)">
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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. ...
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Self-dual embeddings of complete bipartite graphs
<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>
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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 ...
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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>
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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 ...
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Matroids Determine the Embeddability of Graphs in Surfaces
<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>
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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. ...
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Matroids determine the embeddability of graphs in surfaces
<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>
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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. ...
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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>
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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. ...
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Maximum genus embeddings of Steiner triple systems
<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>
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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. ...
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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>
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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
<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>
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<span title="2013-05-01">2013</span>
<span class="release-stage" >pre-print</span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1305.0143v1">arXiv:1305.0143v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/c5kpxh4zsrgxpczue2oz5yswdi">fatcat:c5kpxh4zsrgxpczue2oz5yswdi</a> </span>
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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.). ...
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Classification of nonorientable regular embeddings of Hamming graphs
<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>
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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. ...
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On the orientable genus of graphs with bounded nonorientable genus
<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>
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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). ...
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Classification of nonorientable regular embeddings of Hamming graphs
[article]
<span title="2011-07-16">2011</span>
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arXiv
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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. ...
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