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1.
In this paper, we study the rooted nonseparable maps on the sphere and the projective plane with the valency of root-face and the number of edges as parameters. Explicit expression of enumerating functions are obtained for such maps on the sphere and the projective plane. A parametric expression of the generating function is obtained for such maps on the projective plane, from which asymptotic evaluations are derived. Moreover, if the number of edges is sufficiently large, then almost all nonseparable maps on the projective plane are not triangulation. 相似文献
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In this paper, the chromatic sum functions of rooted biloopless nonseparable near-triangulations on the sphere and the projective plane are studied. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of such maps are derived. An asymptotic evaluation and some explicit expression of enumerating functions are also derived. 相似文献
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Zhaoxiang Li 《Discrete Mathematics》2007,307(1):78-87
In this paper, we study the chromatic sum functions of rooted general maps on the sphere and the projective plane. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of rooted loopless maps, bipartite maps and Eulerian maps are also derived. Moreover, some explicit expressions of enumerating functions are also derived. 相似文献
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In this paper, we study the chromatic sum functions of rooted nonseparable near-triangulations on the sphere and the projective plane. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of such maps are derived. Applying chromatic sum theory, the enumerating problem of different sorts maps can be studied, and a new method of enumeration can be obtained. Moreover, an asymptotic evaluation and some explicit expression of enumerating functions are also derived. 相似文献
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Zhaoxiang Li Erling Wei Jie Xu Yanpei Liu 《Journal of Applied Mathematics and Computing》2010,34(1-2):71-80
This paper provides the chromatic sum function equations of rooted 2-edge-connected maps on the projective plane. The enumerating function equations of rooted 2-edge-connected loopless maps and rooted 2-edge-connected bipartite maps on the projective plane are derived by the chromatic sum function equation of rooted 2-edge-connected maps on the projective plane. 相似文献
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Enumeration of maps on the projective plane 总被引:1,自引:0,他引:1
1. IntroductionA lnap is rooted if an edge is distinguished togetl1er with an end and a side of the edge.An edge belo11ging to only one face is called double (or 8ingular by some author), al1 othersbelonging to exactly two faces are called s1ngle. The enumeration of rooted p1anar maps wasfirst introduced by Tutte['], Techniques originated by Tutte [2,3l for enumerating variousclasses of rooted Inaps on tIle sphere are here applied to the c1asses of alI rooted maps onthe projective plane. Th… 相似文献
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In this paper we study the chromatic sum functions for rooted nonseparable near-triangular maps on the projective plane. A chromatic sum equation for such maps is obtained. 相似文献
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The nonrevisiting path conjecture for polytopes, which is equivalent to the Hirsch conjecture, is open. However, for surfaces,
the nonrevisiting path conjecture is known to be true for polyhedral maps on the sphere, projective plane, torus, and a Klein
bottle. Barnette has provided counterexamples on the orientable surface of genus 8 and nonorientable surface of genus 16.
In this note the question is settled for all the remaining surface except the connected sum of three copies of the projective
plane. 相似文献
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A map is singular if each edge is on the same face on a sruface (i.e., those have only one face on a surface). Because any map with loop is not colorable, all maps here are assumed to be loopless. In this paper povides the explicit expression of chromatic sum functions for rooted singular maps on the projective plane, the torus and the Klein bottle. From the explicit expression of chromatic sum functions of such maps, the explicit expression of enum erating functions of such maps are also derived. 相似文献
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1IntroductionAsurfaceisacompactclosed2-manifold.Theorielltable(non-orielltable)surfaceofgenuskisthespherewitllkhandles(crosscaPs)denotedbySk(Nk).AmapMollSk(Nk)meansthatitsunderlyinggraphnlaybedrownou(embeddedin)itsuchthatllthpairofedgesintersectataninnerpoilltalldeachfaceishomeomorphictothedisc.Amapisrootedifanedgewithadirectiollalongtheedge,alldasideoftl1eedgeisdistinguisl1ed.Tworootedmapsareconsideredtobethesal11eifthereisanisomorphismpreserviIlgtl1erooting.ArootedEuleriall1llapissuchaon… 相似文献
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V. A. Voblyi 《Mathematical Notes》2008,83(1-2):14-22
Two combinatorial identities obtained by the author are used to simplify formulas for the number of general rooted cubic planar maps, for the number of g-essential maps on surfaces of small genus, and also for rooted Eulerian maps on the projective plane. Besides, an asymptotics for the number of maps with a large number of vertices is obtained. 相似文献
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Lszl Babai 《Journal of Graph Theory》1991,15(6):587-627
We consider vertex-transitive graphs embeddable on a fixed surface. We prove that all but a finite number of them admit embeddings as vertex-transitive maps on surfaces of nonnegative Euler characteristic (sphere, projective plane, torus, or Klein bottle). It follows that with the exception of the cycles and a finite number of additional graphs, they are factor graphs of semiregular plane tilings. The results generalize previous work on the genus of minimal Cayley graphs by V. Proulx and T. W. Tucker and were obtained independently by C. Thomassen, with significant differences in the methods used. Our method is based on an excursion into the infinite. The local structure of our finite graphs is studied via a pointwise limit construction, and the infinite vertex-transitive graphs obtained as such limits are classified by their connectivity and the number of ends. In two appendices, we derive a combinatorial version of Hurwitz's Theorem, and classify the vertex-transitive maps on the Klein bottle. 相似文献
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In this paper we study the chromatic sum functions for rooted nonseparable simple maps on the plane. The chromatic sum function equation for such maps is obtained. The enumerating function equation of such maps is derived by the chromatic sum equation of such maps. From the chromatic sum equation of such maps, the enumerating function equation of rooted nonseparable simple bipartite maps on the plane is also derived. 相似文献
16.
Reducing Dehn Fillings and Small Surfaces 总被引:1,自引:0,他引:1
Lee Sangyop; Oh Seungsang; Teragaito Masakazu 《Proceedings London Mathematical Society》2006,92(1):203-223
In this paper we investigate the distances between Dehn fillingson a hyperbolic 3-manifold that yield 3-manifolds containingessential small surfaces including non-orientable surfaces.In particular, we study the situations where one filling createsan essential sphere or projective plane, and the other createsan essential sphere, projective plane, annulus, Möbiusband, torus or Klein bottle, for all eleven pairs of such non-hyperbolicmanifolds. 2000 Mathematics Subject Classification 57M50. 相似文献
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众所周知,由于本质圈(或不可收缩圈)的作用,使得一般的曲面上要得到带有两到三个参数的地图计算公式(尤其是显式公式)变得十分困难。该文集中讨论射影平面上不可分近三角剖分地图的计算。通过引入含有面次,边数和内部面数的参数表达式与Lagrangian反演,作者得到了含有正项系数的显式公式用以计算射影平面上三角剖分地图 。 相似文献
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It is well known that regular maps exist on the projective plane but not on the Klein bottle, nor the non-orientable surface of genus 3. In this paper several infinite families of regular maps are constructed to show that such maps exist on non-orientable surfaces of over 77 per cent of all possible genera. 相似文献
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本文研究了平面上一般带根地图的色和与双色和,得到了这类地图的色和与双色和函数方程。从这类地图的色和函数方程,导出了平面上一般无环地图、平面上二部地图和平面上欧拉地图的计数函数方程。还得到了一些计数函数的计数显式。 相似文献
20.
We classify maps which preserve orthogonality on the Cayley projective plane over octonions. In addition, we also classify orthogonality preserving maps on finite dimensional projective spaces over reals, complexes, or quaternions. Unlike similar results which extend Uhlhorns’s theorem we assume neither injectivity/surjectivity nor that orthogonality is preserved in both directions. 相似文献