共查询到20条相似文献,搜索用时 15 毫秒
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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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Based on the joint tree model introduced by Liu, the genera of further types of graphs not necessary to have certain symmetry can be obtained. In this paper, we obtain the genus of a new type of graph with weak symmetry. As a corollary, the genus of complete tripartite graph K n,n,l (l≥n≥2) is also derived. The method used here is more direct than those methods, such as current graph, used to calculate the genus of a graph and can be realized in polynomial time. 相似文献
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§ 1.Introduction Intopologicalgraphtheory ,agraphmayhavemultipleadjacentiesandselfloops.Agraphiscalledsimplicialifithasnomultipleadjacenciesandselfloops .Asurfacehereisacompact2 manifoldwithoutboundary .Anembeddingofagraphiscellularifeachcomponentofthesur… 相似文献
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There are many results on the maximum genus, among which most are written for the existence of values of such embeddings,
and few attention has been paid to the estimation of such embeddings and their applications. In this paper we study the number
of maximum genus embeddings for a graph and find an exponential lower bound for such numbers. Our results show that in general
case, a simple connected graph has exponentially many distinct maximum genus embeddings. In particular, a connected cubic
graph G of order n always has at least distinct maximum genus embeddings, where α and m denote, respectively, the number of inner vertices and odd components of an optimal tree T. What surprise us most is that such two extremal embeddings (i.e., the maximum genus embeddings and the genus embeddings)
are sometimes closely related with each other. In fact, as applications, we show that for a sufficient large natural number
n, there are at least many genus embeddings for complete graph K
n
with n ≡ 4, 7, 10 (mod12), where C is a constance depending on the value of n of residue 12. These results improve the bounds obtained by Korzhik and Voss and the methods used here are much simpler and
straight.
This work was supported by the National Natural Science Foundation of China (Grant No. 10671073), Science and Technology commission
of Shanghai Municipality (Grant No. 07XD14011) and Shanghai Leading Academic Discipline Project (Grant No. B407) 相似文献
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Maximum Genus of Strong Embeddings 总被引:4,自引:0,他引:4
Er-lingWei Yan-peiLiu HanRen 《应用数学学报(英文版)》2003,19(3):437-446
The strong embedding conjecture states that any 2-connected graph has a strong embedding on some surface. It implies the circuit double cover conjecture: Any 2-connected graph has a circuit double cover.Conversely, it is not true. But for a 3-regular graph, the two conjectures are equivalent. In this paper, a characterization of graphs having a strong embedding with exactly 3 faces, which is the strong embedding of maximum genus, is given. In addition, some graphs with the property are provided. More generally, an upper bound of the maximum genus of strong embeddings of a graph is presented too. Lastly, it is shown that the interpolation theorem is true to planar Halin graph. 相似文献
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研究了不可定向曲面上最大亏格嵌入的估计数,得到了几类图的指数级不可定向最大亏格嵌入的估计数的下界.利用电流图理论,证明了完全图K_(12s)在不可定向曲面上至少有2~(3s-1)个最小亏格嵌入;完全图K_(12s+3)在不可定向曲面上至少有2~(2s)个最小亏格嵌入;完全图K_(12s+7)在不可定向曲面上至少有2~(2s+1)个最小亏格嵌入. 相似文献
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The genus distributions for a certain type of permutation graphs in orientable surfaces 总被引:1,自引:0,他引:1
Rong-xia HAO~ 《中国科学A辑(英文版)》2007,50(12):1748-1754
A circuit is a connected nontrivial 2-regular graph.A graph G is a permutation graph over a circuit C,if G can be obtained from two copies of C by joining these two copies with a perfect matching.In this paper,based on the joint tree method introduced by Liu,the genus polynomials for a certain type of permutation graphs in orientable surfaces are given. 相似文献
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In an earlier paper the authors showed that with one exception the nonorientable genus of the graph with m≥n−1, the join of a complete graph with a large edgeless graph, is the same as the nonorientable genus of the spanning subgraph . The orientable genus problem for with m≥n−1 seems to be more difficult, but in this paper we find the orientable genus of some of these graphs. In particular, we determine the genus of when n is even and m≥n, the genus of when n=2p+2 for p≥3 and m≥n−1, and the genus of when n=2p+1 for p≥3 and m≥n+1. In all of these cases the genus is the same as the genus of Km,n, namely ⌈(m−2)(n−2)/4⌉. 相似文献
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Two cellular embeddings i: G → S and j: G → S of a connected graph G into a closed orientable surface S are equivalent if there is an orientation-preserving surface homeomorphism h: S → S such that hi = j. The genus polynomial of a graph G is defined by
$
g\left[ G \right](x) = \sum\limits_{g = 0}^\infty {a_g x^g ,}
$
g\left[ G \right](x) = \sum\limits_{g = 0}^\infty {a_g x^g ,}
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强嵌入猜想称:任意2-连通图都可以强嵌入到某一曲面上.本文通过分析极大外平面图的结构以及强嵌入的特征,讨论了该图类的不可定向强最大亏格,并给出了一个复杂度为O(nlogn)的算法.其中部分图类的强最大亏格嵌入提供该图的一个少双圈覆盖. 相似文献
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Yoshiaki Fukuma 《Geometriae Dedicata》1997,64(2):229-251
Let (X,L) be a quasi-polarized variety, i.e. X is a smooth projective variety over the complex numbers
and L is a nef and big divisor on X. Then we conjecture that g(L) = q(X), whereg(L) is the sectional genus of L and
. In this paper, we treat the case
. First we prove that this conjecture is true for
, and we classify (X,L) withg(L)=q(X), where
is the Kodaira dimension of X. Next we study some special cases of
. 相似文献
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A diagram D of a knot defines the corresponding Gauss Diagram G
D
. However, not all Gauss diagrams correspond to the ordinary knot diagrams. From a Gauss diagram G we construct closed surfaces F
G
and S
G
in two different ways, and we show that if the Gauss diagram corresponds to an ordinary knot diagram D, then their genus is the genus of the canonical Seifert surface associated to D. Using these constructions we introduce the virtual canonical genus invariant of a virtual knot and find estimates on the number of alternating knots of given genus and given crossing number. 相似文献
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