Wm∨Pn的交叉数

在Klesc M给出的联图W_3 V P_n的交叉数的基础上,继续对联图Wm V Pn（m=4,5）的交叉数cr进行了研究,得到了cr（W3 V Pn）=Z（5,n）＋n＋「n/2＋1」以及cr（W5 V Pn）=Z（6,n）＋n＋3[n/2」＋1,n≥2.     

极大平面图在不可定向曲面上强嵌入的一个注记

§ 1　IntroductionA strong embeddingμ( G) of a graph G in a surface S is such an embedding thateachface boundary of the surface is a circuit.( A strong embedding is also sometimes called acircular embedding,see[1 ] orclosed2 -cell embedding[2 ] ) .Graphsconsidered here are sim-ple( that is,they have no loops or multiple edges) .Terminology here follows those in[3] .In[1 ] ,Richter,Seymour and Siran proved that every3-connected planar graph canbe strongly embedded on some non-orientable sur…     

关于点的度在modulo下等值的上可嵌入图类

结合４－边形２－因子条件,确定了一类点的度在ｍｏｄｕｌｏ４下值为０,１的上可嵌入图类,从而综合已有的结果,较完整地刻划了这类图的上可嵌入性情况。     

$W_m$与$P_n$ 的笛卡儿积图的交叉数

Most results on crossing numbers of graphs focus on some special graphs, such as the Cartesian products of small graphs with path, star and cycle. In this paper, we obtain the crossing number formula of Cartesian products of wheel Wm with path Pn, for arbitrary m ≥ 3 and n≥ 1.     

与顶点A-划分有关的上可嵌入图类

图G的顶点A-划分是指:G的顶点集划分{V1,V2,···,Vs},其中G[Vi](1≤i≤s)为多重完全图或多重完全二部图.文中结合图的顶点A-划分,顶点度及边连通性等条件确定了一些新的上可嵌入图类,从而将已有类似结果进行了推广,且完整地刻画了这类图的上可嵌入性情况.     

平面图的理论与四色问题(Ⅲ)——由四色问题引出的理论工作

在§10中讨论了研究平面图的面着色只需考查范平面图。且由定理10.5,将四色问题化为确定如下模3方程是否有全非0(mod3)解的问题:     

ON THE NUMBER OF EULERIAN PLANAR MAPS

This paper presents the number of combinatorially distinct rooted Eulerian planar maps with the number of non-root-vertices and the number of non-root-faces as two parameters. The parametric expressions for determining the number in the loopless Eulerian case are also obtained.     

环面上近三角剖分地图的计数

本文提供了环面上带边数和根面次这两个参数的有根近三角剖分的函数方程及其参数表达式，并给出了根面次为1以边数为参数的有根近三角剖分地图的精确解．     

3,4跳图的平面性

For a graph G of size ε≥1 and its edge-induced subgraphs H1 and H2 of size r(1≤r≤ε), H1 is said to be obtained from H2 by an edge jump if there exist four distinct vertices u,v,w and x in G such that (u,v)∈E(H2), (w,x)∈ E(G)-E(H2) and H1=H2-(u,v)+(w,x). In this article, the r-jump graphs (r≥3) are discussed. A graph H is said to be an r-jump graph of G if its vertices correspond to the edge induced graph of size r in G and two vertices are adjacent if and only if one of the two corresponding subgraphs can be obtained from the other by an edge jump. For k≥2, the k-th iterated r-jump graph Jrk(G) is defined as Jr(Jrk-1(G)), where Jr1(G)=Jr(G).An infinite sequence{Gi} of graphs is planar if every graph Gi is planar. It is shown that there does not exist a graph G for which the sequence {J3k(G)} is planar, where k is any positive integer. Meanwhile,lim gen(J3k(G))=∞,where gen(G) denotes the genus of a graph G, if the sequencek→∞J3k(G) is defined for every positive integer k. As for the 4-jump gra     

SOME CLASSES OF UPPER EMBEDDABLE GRAPHS

1IntroductionSincetheintroductoryinvestigationofmaximumgenusbyNordhaus,Stewart,andWhite[3],theupperembeddabilityofgraphshasreceivedgreatemphasissofar.AlthoughLiu[16]andNebesky[9]haverespectivelyprovideddifferentnecessaryandsufficientconditionsontheupperembeddabilityofgraphs,weknowlessaboutwhatclassesofgraphsareupperembeddable.Jaeger,PayanandXuong[10]provedthateverygraphobtainedbyconnecting(withanynumberofedges)twovertex-disjointupperembeddablegraphswithevenBettinumberisupperembeddable.Skov…