共查询到18条相似文献,搜索用时 250 毫秒
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一个近-三角剖分嵌入是指一个曲面上的嵌入图使得几乎所有的面都是三角形,至多只有一个可能的例外.文中作者证明了如下结论:如果一个图G 在球面S0(或环面S1)上有近-三角剖分嵌入,那么G在每一个可定向曲面Sk有近-三角剖分嵌入,其中k=h,h+1,\cdots ,\lfloor\frac{\beta(G)}{2}\rfloor$, 而h=0(或1)并且β(G)是图G的Betti数.特别地,G是上可嵌入的. 相似文献
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两类四正则图的完全亏格分布 总被引:3,自引:2,他引:1
一个图G的完全亏格多项式表征了图G的亏格(可定向,不可定向)分布情况.本文利用刘彦佩提出的嵌入的联树模型,得出了两类新的四正则图的完全亏格多项式,并推导出已有结果的两类图的完全亏格多项式.此处的结果形式更为简单. 相似文献
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广义 Petersen 图 P(n, m) 是这样的一个图:它的顶点集是{ui, vi | i=0,1, … , n-1}, 边集是 {uiui+1, vivi+m, uivi | i=0,1, …, n-1}, 这里 m, n 是正整数、加法是在模n 下且 m<|n/2| . 这篇文章证明了P(2m+1, m)(m≥ 2) 的 Euler 亏格是1, 并且 P(2m+2, m)(m≥ 5) 的 Euler 亏格是2. 相似文献
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图在曲面上嵌入的分类就是确定图在同一曲面上(不等价的)嵌入的数目.本文,利用刘彦佩提出的嵌入的联树模型,得到了双极图与扇图的关联曲面之间的关系,进而由已知结论的双极图的亏格分布和完全亏格分布推导出扇图的亏格分布和完全亏格分布,并给出了扇图在亏格为1-4的不可定向曲面上嵌入的个数的显式. 相似文献
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陈仪朝等运用覆盖矩阵和Chebyshev多项式计算了一些图类在曲面上的亏格分布,本文给出了一类不能运用Chebyshev多项式的类循环图,计算出它在可定向曲面上的嵌入. 相似文献
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There is a Group of Every Strong Symmetric Genus 总被引:1,自引:0,他引:1
Let G be a finite group. The strong symmetric genus 0(G) isthe minimum genus of any Riemann surface on which G acts, preservingorientation. For any non-negative integer g, there is at leastone group of strong symmetric genus g. For g2, one such grouphas the form Zk x Dn for some k and n. 2000 Mathematics SubjectClassification 57M60 (primary), 20H10, 30F99 (secondary). 相似文献
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Enric Nart 《Advances in Mathematics》2009,221(3):774-787
We find a closed formula for the number hyp(g) of hyperelliptic curves of genus g over a finite field k=Fq of odd characteristic. These numbers hyp(g) are expressed as a polynomial in q with integer coefficients that depend on g and the set of divisors of q−1 and q+1. As a by-product we obtain a closed formula for the number of self-dual curves of genus g. A hyperelliptic curve is defined to be self-dual if it is k-isomorphic to its own hyperelliptic twist. 相似文献
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A graph G homogeneously embeds in a graph H if for every vertex x of G and every vertex y of H there is an induced copy of G in H with x at y. The graph G uniformly embeds in H if for every vertex y of H there is an induced copy of G in H containing y. For positive integer k, let fk(G) (respectively, gk(G)) be the minimum order of a graph H whose edges can be k-coloured such that for each colour, G homogeneously embeds (respectively, uniformly embeds) in the graph given by V(H) and the edges of that colour. We investigate the values f2(G) and g2(G) for special classes of G, in particular when G is a star or balanced complete bipartite graph. Then we investigate fk(G) and gk(G) when k ≥ 3 and G is a complete graph. 相似文献
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Edward R. Scheinerman 《Journal of Graph Theory》1987,11(3):441-446
The interval number of a graph G, denoted i(G), is the least positive integer t such that G is the intersection graph of sets, each of which is the union of t compact real intervals. It is known that every planar graph has interval number at most 3 and that this result is best possible. We investigate the maximum value of the interval number for graphs with higher genus and show that the maximum value of the interval number of graphs with genus g is between ?√g? and 3 + ?√3g?. We also show that the maximum arboricity of graphs with genus g is either 1 + ?√3g? or 2 + ?√3g?. 相似文献
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In an earlier work, the second author proved a general formulafor the equivariant Poincaré polynomial of a linear transformationg which normalises a unitary reflection group G, acting on thecohomology of the corresponding hyperplane complement. Thisformula involves a certain function (called a Z-function below)on the centraliser CG(g), which was proved to exist only incertain cases, for example, when g is a reflection, or is G-regular,or when the centraliser is cyclic. In this work we prove theexistence of Z-functions in full generality. Applications includereduction and product formulae for the equivariant Poincarépolynomials. The method is to study the poset L(CG(g)) of subspaceswhich are fixed points of elements of CG(g). We show that thisposet has Euler characteristic 1, which is the key propertyrequired for the definition of a Z-function. The fact aboutthe Euler characteristic in turn follows from the join-atomproperty of L(CG(g)), which asserts that if [X1,..., Xk} isany set of elements of L(CG(g)) which are maximal (set theoretically)then their setwise intersection lies in L(CG(g)). 2000 Mathematical Subject Classification:primary 14R20, 55R80; secondary 20C33, 20G40. 相似文献
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A relative embedding of a connected graph is an embedding of the graph in some surface with respect to some closed walks,
each of which bounds a face of the embedding. The relative maximum genus of a connected graph is the maximum of integerk with the property that the graph has a relative embedding in the orientable surface withk handles. A polynomial algorithm is provided for constructing relative maximum genus embedding of a graph if the relative
tree of the graph is planar. Under this condition, just like maximum genus embedding, a graph does not have any locally strict
maximum genus. 相似文献
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本文证明了:对于任何一个有圈连通图G,其不可定向最大亏格为这里,α0,α1分别为G的顶点和边的数目.从而,也解决了图的不可定向嵌入的存在性问题. 相似文献
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A (k,g)-Cayley cage is a k-regular Cayley graph of girth g and smallest possible order. We present an explicit construction of (k,g)-Cayley graphs for all parameters k≥2 and g≥3 and generalize this construction to show that many well-known small k-regular graphs of girth g can be constructed in this way. We also establish connections between this construction and topological graph theory, and address the question of the order of (k,g)-Cayley cages. 相似文献