共查询到20条相似文献,搜索用时 140 毫秒
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图G的一个圆环r-染色(r≥2)是将G的每个顶点v对应到一个周长为r的圆上的点的一个映射f,使得对于G中任意的边xy,f(x)和f(y)在圆上的距离不小于1.G的圆环色数χc(G)是G存在圆环r-染色的最小实数r.符号图的圆环染色和图的圆环染色基本相同,不同的是对于负边xy,我们要求f(x)和f(y)的对点在圆上的距离不小于1.符号图(G,σ)的圆环色数是使得(G,σ)在圆环r-染色的最小实数r.本文证明:对于任意正整数k和实数ε> 0,存在整数g使得对于任意树宽至多为k的符号图(G,σ),如果(G,-σ)的负围长至少是g,那么(G,σ)的圆环染色数至多是2+ε. 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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图G的正常边染色f满足相邻点的色集合相不互包含时,该染色称为图G的Smarandcchely-邻点可区别边染色,其中S(x)={f(xw)|xw∈E(G)}称之为在f下的顶点x的色集合.该染色称为图G的Smarandchely-邻点可区别边染色.对图G进行的.Smarandchely-邻点可区别边染色所用最少颜色数称为图G的Smarandachely-邻点可区别边色数.讨论了Pm□Pn的Smarandchely-邻点可区别边色数. 相似文献
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Brooks证明了:若G是连通的简单图,并且它既不是奇圈,又不是完全图,那么它的色数至多为△(G),其中△(G)为图G的最大度.它可以推出嵌入到Klein瓶上的任意的一个6-正则图的色数至多为6.通过对Klein瓶上的6-正则嵌入图的结构分析,证明了Klein瓶上的任意的一个6-正则嵌入图的色数为5. 相似文献
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《数学的实践与认识》2013,(23)
图G的一个正常边染色被称作邻点可区别无圈边染色,如果G中无二色圈,且相邻点关联边的色集合不同.图G的邻点可区别无圈边色数记为χ′_(aa)(G),即图G的一个邻点可区别无圈边染色所用的最少颜色数.通过构造具体染色的方法,给出了一些k-方图的邻点可区别无圈边色数. 相似文献
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设H是阶为n的连通图.在H的某一个顶点上悬挂一棵阶为j的树,得到图H_j,用H_j表示这样的图形族.本文证明:当j充分大时,有r(G,H_j)=(x(G)-1)(n+j-1)+s(G),其中x(G),s(G)分别表示图G的色数和色数剩余. 相似文献
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图G的一个无圈边着色是一个正常的边着色且不含双色的圈.图G的无圈边色数是图G的无圈边着色中所用色数的最小者.本文用反证法得到了不含5-圈的平面图G的无圈边色数的一个上界. 相似文献
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本文证明了3-连通非偶图的色多项式根2的阶为1;满足一定条件的非3-连通非偶图的色多项式根2的阶是图的非偶块和非偶可分块数.从而,把色多项式P(G)中1的阶是图G的非平凡块数这一结果进一步加以推广. 相似文献
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刘红美 《数学物理学报(B辑英文版)》2006,26(2):314-320
For a general graph G, M(G) denotes its Mycielski graph. This article gives a number of new sufficient conditions for G to have the circular chromatic number Xc(M(G)) equals to the chromatic number X(M(G)), which have improved some best sufficient conditions published up to date. 相似文献
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Mycielski图是在1955年由Mycielski首先提出的,推广的Mycielski图是在2003年由Peter Che Bor Lam,林文松等给出的Mycielski图的一个自然推广,且研究了它的圆色数.目前关于推广的Mycielski图性质以及它们在点色数,分数色数,圆色数等方面已有许多研究.本文定义了推广的Mycielski图的另一推广称为类推广的Mycielski图,且探讨了推广的Mycielski图和类推广的Mycielski图在全染色、邻点可区别全染色方面与原基础图的关系,从而也得到了它们满足全染色猜想和邻点可区别全染色猜想及它们达到全色数和邻点可区别的全色数的下界的一些充分条件. 相似文献
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The fractional and circular chromatic numbers are the two most studied non-integral refinements of the chromatic number of a graph. Starting from the definition of a coloring base of a graph, which originated in work related to ergodic theory, we formalize the notion of a gyrocoloring of a graph: the vertices are colored by translates of a single Borel set in the circle group, and neighboring vertices receive disjoint translates. The corresponding gyrochromatic number of a graph always lies between the fractional chromatic number and the circular chromatic number. We investigate basic properties of gyrocolorings. In particular, we construct examples of graphs whose gyrochromatic number is strictly between the fractional chromatic number and the circular chromatic number. We also establish several equivalent definitions of the gyrochromatic number, including a version involving all finite abelian groups. 相似文献
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Eric Sopena 《Journal of Graph Theory》1997,25(3):191-205
We introduce in this paper the notion of the chromatic number of an oriented graph G (that is of an antisymmetric directed graph) defined as the minimum order of an oriented graph H such that G admits a homomorphism to H. We study the chromatic number of oriented k-trees and of oriented graphs with bounded degree. We show that there exist oriented k-trees with chromatic number at least 2k+1 - 1 and that every oriented k-tree has chromatic number at most (k + 1) × 2k. For 2-trees and 3-trees we decrease these upper bounds respectively to 7 and 16 and show that these new bounds are tight. As a particular case, we obtain that oriented outerplanar graphs have chromatic number at most 7 and that this bound is tight too. We then show that every oriented graph with maximum degree k has chromatic number at most (2k - 1) × 22k-2. For oriented graphs with maximum degree 2 we decrease this bound to 5 and show that this new bound is tight. For oriented graphs with maximum degree 3 we decrease this bound to 16 and conjecture that there exists no such connected graph with chromatic number greater than 7. © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 191–205, 1997 相似文献
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The circular choosability or circular list chromatic number of a graph is a list-version of the circular chromatic number, that was introduced by Mohar in 2002 and has been studied by several groups of authors since then. One of the nice properties that the circular chromatic number enjoys is that it is a rational number for all finite graphs G, and a fundamental question, posed by Zhu and reiterated by others, is whether the same holds for the circular choosability. In this paper we show that this is indeed the case. 相似文献
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In this article, we consider the circular chromatic number χc(G) of series‐parallel graphs G. It is well known that series‐parallel graphs have chromatic number at most 3. Hence, their circular chromatic numbers are at most 3. If a series‐parallel graph G contains a triangle, then both the chromatic number and the circular chromatic number of G are indeed equal to 3. We shall show that if a series‐parallel graph G has girth at least 2 ⌊(3k − 1)/2⌋, then χc(G) ≤ 4k/(2k − 1). The special case k = 2 of this result implies that a triangle free series‐parallel graph G has circular chromatic number at most 8/3. Therefore, the circular chromatic number of a series‐parallel graph (and of a K4‐minor free graph) is either 3 or at most 8/3. This is in sharp contrast to recent results of Moser [5] and Zhu [14], which imply that the circular chromatic number of K5‐minor free graphs are precisely all rational numbers in the interval [2, 4]. We shall also construct examples to demonstrate the sharpness of the bound given in this article. © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 14–24, 2000 相似文献
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循环着色是普通着色的推广.本文中,我们研究了一类平面图-“花图”的循环着色问题,证明了由2r 1个长为2n 1的圈构成的“辐路”长度为m的花图Fr,m,n的循环色数是2 1/(n-m/2),并证明了在这类图中去掉任何一个点或边后,循环色数都严格减少但普通色数不减少,即这类图是循环色临界的但不是普通色临界的.同时,我们还研究了循环着色与图Gkd中的链之间的关系,给出了两个等价的条件. 相似文献