共查询到20条相似文献,搜索用时 93 毫秒
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设G是一个图,其边集是E(G),E(G)是一个子集S称为G的一个边覆盖,若G是每一点都是S中一条边的端点,G的一个(正常)边覆盖染色是对G的边进行染色,使得每一色组都是G的一个边覆盖,使G有(正常)边覆盖染色所需最多颜色数,称为G的边覆盖色数,用X′c(G)表示,已知的结果是对于任意简单图G,都有δ-1≤X′c(G)≤X∧2,(G)≤δ,δ是G的最小度,若X∧2c(G)=δ,则称G是CI类的,否则称为CII类的,本文主要研究了平面图及平衡的安全r分图的分类问题。 相似文献
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对于图G(V,E)的正常k-全染色φ称为G(V,E)的k-均匀全染色,当且仅当任意两个色类中的元素总数至多相差1.xvee(G)=m in{k存在图G的一个k-均匀全染色}称为G的均匀全色数.本文得到了两类M ycielsk i图及圈,轮图和扇形的均匀全色数. 相似文献
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《数学的实践与认识》2017,(24)
如果图G的一个正常顶点染色满足任两个色类中的顶点数相差不超过1,则称为G的均匀染色.研究了一些Mycielski图的均匀染色,给出了路、圈、完全图和广义星图的Mycielski图的均匀色数. 相似文献
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图的边覆盖染色中的分类问题(英文) 总被引:1,自引:0,他引:1
设 G是一个图 ,其边集是 E( G) ,E( G)的一个子集 S称为 G的一个边覆盖 ,若 G的每一点都是 S中一条边的端点 .G的一个 (正常 )边覆盖染色是对 G的边进行染色 ,使得每一色组都是 G的一个边覆盖 ,使 G有 (正常 )边覆盖染色所需最多颜色数 ,称为 G的边覆盖色数 ,用χ′c( G)表示 .已知的结果是对于任意简单图 G,都有 δ- 1≤ χ′c( G)≤ δ,δ是 G的最小度 .若 χ′c( G) =δ,则称 G是 CI类的 ;否则称为 CII类的 .本文主要研究了平面图及平衡的完全 r分图的分类问题 相似文献
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边覆盖临界图的一些性质 总被引:2,自引:0,他引:2
设G是一个简单图,其顶点集为V(G)而边集为E(G),S∈E(G)称为 G的一个覆盖,如果由S导出的子图为G的一个生成子图. G的边覆盖色数χ'c(G)是E(G,)所能划分成的最大边覆盖数.已知δ-1 ≤χ'c(G)≤δ,由此将χ'c(G)=δ的图称为CI类图,否则称为CII类图.若G是连通CII类图,且G不是完全图,对任意的u,u∈V(G),e=uv( )E(G),都有χ'c(G+e)>χ'c(G)成立,则称G为边覆盖临界的.本文研究了边覆盖临界图的一些性质.即若G为边覆盖临界图,则对任意的u,v∈V(G),若e=uv( )E(G),总存在w∈{u,v},有d(w)≤2δ-2,且w至少与max{d(w)-δ+1,3d(w)-4δ+4}个最小度顶点相邻. 相似文献
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路与完全图的笛卡尔积图和广义图K(n,m)的关联色数 总被引:4,自引:0,他引:4
Richrd A.Brualdi和J.Quinn Massey在[1]中引入了图的关联着色概念,并且提出了关联着色猜想,即每一个图G都可以用△(G)+2种色正常关联着色.B.Guiduli[2]说明关联着色的概念是I.Algor和N.Alon[3]提出的有向星荫度的一个特殊情况,并证实[1]的关联着色猜想是错的,给出图G的关联色数的一个新的上界是△(G)+O(Log(△G)).[4]确定了某些特殊图类的关联色数.本文给出了路和完全图的笛卡尔积图的关联色数,而且利用此结果又确定了完全图Kn的广义图K(n,m)的关联色数. 相似文献
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完全三部图K(n_1,n_2,n_3)的色唯一性 总被引:4,自引:0,他引:4
设G是简单图,用P(G,λ)表示图G的色多项式.若对任意简单图H使P(H,λ)=P(G,λ),都有H与G同构,则称G是色唯一图.令K(n 相似文献
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Roots of graph polynomials such as the characteristic polynomial, the chromatic polynomial, the matching polynomial, and many others are widely studied. In this paper we examine to what extent the location of these roots reflects the graph theoretic properties of the underlying graph. 相似文献
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如果图G的一个正常染色满足染任意两种颜色的顶点集合导出的子图是一些点不交的路的并,则称这个正常染色为图G的线性染色.图G的线性色数用lc(G)表示,是指G的所有线性染色中所用的最少颜色的个数.证明了:若G是一个最大度△(G)≠5,6的平面图,则lc(G)≤2△(G). 相似文献
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《Annals of Pure and Applied Logic》2019,170(9):1030-1069
Graph polynomials are graph parameters invariant under graph isomorphisms which take values in a polynomial ring with a fixed finite number of indeterminates. We study graph polynomials from a model theoretic point of view. In this paper we distinguish between the graph theoretic (semantic) and the algebraic (syntactic) meaning of graph polynomials. Graph polynomials appear in the literature either as generating functions, as generalized chromatic polynomials, or as polynomials derived via determinants of adjacency or Laplacian matrices. We show that these forms are mutually incomparable, and propose a unified framework based on definability in Second Order Logic. We show that this comprises virtually all examples of graph polynomials with a fixed finite set of indeterminates. Finally we show that the location of zeros and stability of graph polynomials is not a semantic property. The paper emphasizes a model theoretic view. It gives a unified exposition of classical results in algebraic combinatorics together with new and some of our previously obtained results scattered in the graph theoretic literature. 相似文献
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王国兴 《数学的实践与认识》2014,(21)
图G的正常边染色称为是点可区别的,如果对G的任意两顶点的关联边的颜色构成的集合不同.对图G进行点可区别正常边染色所需要的最少颜色数称为图G的点可区别正常边色数,记为x_s'(G).给出了3阶空图与t阶完全图的联图的点可区别正常边色数. 相似文献
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Xiang-En Chen 《数学研究通讯:英文版》2016,32(4):359-374
Let G be a simple graph. A total coloring f of G is called an E-total coloring if no two adjacent vertices of G receive the same color, and no edge of G receives the same color as one of its endpoints. For an E-total coloring f of a graph G and any vertex x of G, let C(x) denote the set of colors of vertex x and of the edges incident with x, we call C(x) the color set of x. If C(u)≠ C(v) for any two different vertices u and v of V(G), then we say that f is a vertex-distinguishing E-total coloring of G or a VDET coloring of G for short. The minimum number of colors required for a VDET coloring of G is denoted by χ_(vt)~e(G) and is called the VDET chromatic number of G. The VDET coloring of complete bipartite graph K_(7,n)(7 ≤ n ≤ 95) is discussed in this paper and the VDET chromatic number of K_(7,n)(7 ≤ n ≤ 95) has been obtained. 相似文献
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设G(V,E)是阶数至少是3的简单连通图,若f是图G的k-正常边染色,使得对任意的uv∈E(G),C(u)≠C(v),那么称f是图G的k-邻点可区别边染色(k-ASEC),其中C(u)={f(uw)│uw∈E(G)},而χa′s(G)=min{k│存在G的一个k-ASEC},称为G的邻点可区别边色数.本文给出扇的倍图D(Fm)的邻点可区别边色数. 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