A TIGHT LOWER BOUND ON THE MAXIMUM GENUS OF A 3-CONNECTED LOOPLESS MULTIGRAPH

§ 1　 IntroductionA loopless multigraph is a graph having multiple edges but no loops.A multiple ver-tex is a vertex incident with multiple edges.A cubic graph is a graph,each of whose ver-tices is3-valent.A cut-vertex is a vertex of G which will disconnect the graph G if itis re-moved from G.A vertex set C with k vertices is a k-vertex cut setif G-C is disconnectedwhen C is removed.A graph G is k-connected if for any h相似文献   

与最小度有关的图的最大亏格的下界

设Ｇ为简单图且最小度不小于３．结合Ｇ边连通性,文中分别给出了与最小度有关的Ｇ的最大亏格的下界表达式。     

9个经典Ramsey数R(3,t)的新下界

本文研究了经典Ramsey数R(3,t)的下界问题.利用素数阶循环图的性质改进一般阶循环图团数的计算方法,获得了9个经典Ramsey数R(3,t)的新下界:R(3,29)≥183,R(3,30)≥189,R(3,32)≥213,R(3,33)≥218,R(3,34)≥226,R(3,35)≥231,R(3,36)≥239,R(3,37)≥244,R(3,38)≥256,其中前三个结果分别改进了迄今已知的最好的下界,后6个结果是本文首次报道的.     

MAXIMUM GENUS, INDEPENDENCE NUMBER AND GIRTH

1.IntroductionThegraphconsideredhereisconnectedandsimpleunlessstatedotherwise.Forterminologyandnotationwithoutexplanation,wereferto[l].Inthispaperwestudythemaximumgenusofagraph,aninvariancethatcharacterizesthegraphcellularlyembeddedinanorielltablesurface.Recallthatthemaximumgenussdenotedby7M(G),ofthegraphGisthemaximumintegernumberkwiththepropertythatthereexistsacellularembeddingofGontheorientablesurfaceSofgenusk.TheEulerpolyhedralequationshowsthatthemaximumgenusofanygraphGsatisfiesthefollo…     

图的最大亏格与图的着色数

结合边连通性,本文给出了一个图的Ｂｅｔｔｉ亏数由这个图的补图的着色数所确定的上界式,证明了所给出的上界式是最好的,得到关于图的最大亏格下界的若干新结果．     

关于图的下完美邻域数的上界一些结果

本文主要讨论了图的下完美邻域数 ,并给出了θ(G) =γ(G)的充分必要条件 ,并讨论了一些特殊图类的下完美邻域数的上界 ,特别对于树采用了对所有点分层的方法进行了较细致的讨论 ,给出了紧上界θ(T)≤ [n3] .     

用Paley图计算对角Ramsey数下界的新方法

本文研究了对角Paley数的下界问题.利用一个新发现的Paley图的自同构,给出了计算Paley图团数的一个新方法,获得了2个对角Rasey数的新下界:R(20,20)≥18877,R(21,21)≥25949.     

半导体漂移-扩散方程解的上下界整体估计

研究半导体方程解的整体性质,应用Stampacchia的最大模估计方法,证明了解的上下界整体估计.     

Bayes估计的中偏差下界

在某种正则条件下，对Bayes估计尾概率收敛速度问题进行了讨论。利用似然理论方法得到了Bayes估计的中偏差下界，从而改善了Bahadur型的收敛结果。     

关于图的符号控制数的下界

图的符号控制数的研究有许多应用背景，但图的符号控制数的计算是NP完全问题，因而确定其上下界有重大意义。本文在[5]的基础上，引进了新参数δ^*(G)，全面改进了[5]所给出的符号控制数的下界，并给出了一些可达下界的图。     

ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE

The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n ≥ 2. To this end, we first generalize the Carleman’s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna’s representation for harmonic functions in the half sphere by using Hrmander’s theorem.     

UPPER BOUNDS ON THE LOWER OPEN PACKING NUMBER OF A TREE

Abstract

Let G be a graph and let v be a vertex of G. The open neigbourhood N(v) of v is the set of all vertices adjacent with v in G. An open packing of G is a set of vertices whose open neighbourhoods are pairwise disjoint. The lower open packing number of G, denoted ρ^° _L(G), is the minimum cardinality of a maximal open packing of G while the (upper) open packing number of G, denoted ρ^°(G), is the maximum cardinality among all open packings of G. It is known (see [7]) that if G is a connected graph of order n ≥3, then ρ^°(G) ≤ 2n/3 and this bound is sharp (even for trees). As a consequence of this result, we know that ρ^° _L(G) ≤ 2n/3. In this paper, we improve this bound when G is a tree. We show that if G is a tree of order n with radius 3, then ρ^° _L(G) ≤ n/2 + 2 √n-1, and this bound is sharp, while if G is a tree of order n with radius at least 4, then ρ^° _L(G) is bounded above by 2n/3—O√n).     

LOWER BOUND NUMBER OF IRREDUCIBLE GRAPHS ON SURMCES

1IntroductionThesurfaceisacompact2-manifold.AnorientablesurfaCeofgenuskishomeonlorphictoaspherewithkhandles,whichwedenoteitbySk.Anon-orientablesurfaceofgenuskishomeomorphictoaspherewithkcrosscaps,whichwedenoteitbySa.AnembeddingMonsurfaceSgmeanstheunderlyinggraphofMisdrawnonSOsuchthatnoedgesintersecteachotherandeachfaceishomeomorphictothedisc[5],wedenoteitbyMCS,(orforS.).Irreduciblegraphscharacterizethosegraphswhichcannotbeembeddedonasurfacebutdeletinganyedgeofthisgraph,theresultantgraphc…     

(分块)非负矩阵谱半径的界

<正>1引言若A=(a_(ij)),其中a_(ij)≥0,我们则称A为非负矩阵.ρ(A)表示A的谱半径,当A≥0时,ρ(A)就是A的Perron根.众所周知,若A≥0,则r_(min)(A)≤ρ(A)≤r_(max)(A),     

A tight lower bound on the maximum genus of 3-edge connected loopless graphs

1.IntroductionThernchmumgenusl7M(G),ofacormectedgraphG~(V,E)isthem~amongthegenera,amongwhichGhasacellularembeddingonaspherewithkhandles.SinceanyembeddingofGhasatleastonefaCe,byEulerpolyhedralequation,itcanbeobtainedthatwhereP(G)=IE(G)I--IV(G)l IisthecyclerankofG.AgraphGiscalledop-imbeddableif7M(C)=Lop]exactly.Kund.[1]provedthatthereareatleasttWOedge-disjointspanningtreesinGifGis4-edgecormected.LiuandXuongcharacterizedtheuptheeddabilityofgraphsasinthefollowing.Theorem1.112'31.Acorm…     

图的最大亏格、支配数和围长

一个连图G的最大亏格γM（G）=（β（G）-ξ（G）/2,其中β（G）=E（G）-V（G 1是G的圈秩,ξ（G）是G的Betti亏数,本文利用G的支配数和围长给出了G的Betti亏数ξ（G）的一个上界,从而也给出了最大亏格γ（M（G）的一个下界,而且它是可达的,对于某些图类,该下界比黄元秋（2000）所给下界更好。     

矩阵奇异值的下界估计

本文中总记mxn复（实）矩阵空间以C"""（R"""），q二min｛。，n）．设A一（a；。）e＊-"－，A的q个奇异值按递减次序排列为。1川三。2（AZ...Z内科三0．对A的奇异值，特别是最小奇异值的下界估计，是矩阵分析的重要课题，在目前已有重要估计【回叫，C．R．Johnson给出的下述最小奇异值下界估计是最好的结果11］：矩阵Cassini型谱包含域得到了矩阵奇异值的一个下界估计式．进而给出了达到下界估计式时的矩阵表征，所得结果改进了山一［4］之相应结果．我们首先讨论方阵的情况．引理1．设A二（。ti）EC"""，人（）＝｛Al（A），...，A…     

关于特征值的Hoffman-Wielandt型相对扰动界

本文主要研究了关于特征值的Hoffman-wielandt型相对扰动界，改进了LiRC和Ipsen I等人关于这方面的相应结果．     

图的不可定向最大亏格

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.