共查询到19条相似文献,搜索用时 109 毫秒
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图的星色数的概念是Vince在1988年提出的,它是图的色数的一个推广.本文构造了一类星色数是4的平面图. 相似文献
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图的星色数是通常色数概念的推广.本文求出了几类由轮图导出的平面图的星色数.前两类是由3-或5-轮图经细分等构造出的,其星色数分别为2+2/(2n+1),2+3/(3n+1)和2+3/(3n-1).第三类平面图是由n-轮图经过Hajos构造得到的,其星色数为3+1/n.本类图的星色数结果推广了已有结论. 相似文献
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郑国彪 《纯粹数学与应用数学》2012,28(3):294-302
混合超图的上、下色数的研究是超图研究中一个重要的话题.由于超图本身结构上的复杂性,近年来对超图色性的研究也近局限于对一些特殊图类的研究,其中完全一致混合超图是最为热门的图类之一.给出了D完全(C不完全)一致混合超图的概念,并运用组合数学中有关分划的思想和方法对该图类的色性进行了进一步的研究,对相关文献中给出的结论进行了推广,得到了一个较为一般化的结论.并在该定理的证明中得到并证明了一个关于混合超图C稳定集的重要论断,对超图色性研究有着重要的意义. 相似文献
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1988年,Vince定义了图的色数的一个推广——图的星色数,本文研究了有围长限制或有最大度限制的临界图的星色数,得到了三个新结果。 相似文献
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图的限制边连通度是经典边连通度的推广,可用于精确度量网络的容错性.极大限制边连通图是使限制边连通度达到最优的一类图.首先将图的限制边连通度和最小边度的概念推广到r一致线性超图H,证明当H的最小度δ(H)≥r+1时,H的最小边度ξ(H)是它的限制边连通度λ′(H)的一个上界,并将满足ξ(H)=λ′(H)的H称为极大限制边连通超图,然后证明n个顶点的r一致线性超图H如果满足δ(H)≥(n-1)/(2(r-1))+(r-1),则它是极大限制边连通的,最后证明直径为2,围长至少为4的一致线性超图是极大限制边连通的.所得结论是图中相关结果的推广. 相似文献
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本文构造出了星色数为3+1/d,3+2(2d-1),3+3/(3d-1),和3+3/(3d-2)的一些平面图类,从而部分解决了Vince的问题. 相似文献
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J.C Meyer 《Journal of Combinatorial Theory, Series B》1978,24(1):44-50
In this paper, the author defines a hypergraph total chromatic number and determines this number for the complete h-partite and for the complete h-uniform hypergraphs. 相似文献
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Babson and Kozlov (2006) [2] studied Hom-complexes of graphs with a focus on graph colorings. In this paper, we generalize Hom-complexes to r-uniform hypergraphs (with multiplicities) and study them mainly in connection with hypergraph colorings. We reinterpret a result of Alon, Frankl and Lovász (1986) [1] by Hom-complexes and show a hierarchy of known lower bounds for the chromatic numbers of r-uniform hypergraphs (with multiplicities) using Hom-complexes. 相似文献
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Chvátal, Rödl, Szemerédi and Trotter [V. Chvátal, V. Rödl, E. Szemerédi and W.T. Trotter, The Ramsey number of a graph with a bounded maximum degree, J. Combinatorial Theory B 34 (1983), 239–243] proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. In [O. Cooley, N. Fountoulakis, D. Kühn and D. Osthus, 3-uniform hypergraphs of bounded degree have linear Ramsey numbers, submitted] and [B. Nagle, S. Olsen, V. Rödl and M. Schacht, On the Ramsey number of sparse 3-graphs, preprint] the same result was proved for 3-uniform hypergraphs. In [O. Cooley, N. Fountoulakis, D. Kühn and D. Osthus, Embeddings and Ramsey numbers of sparse k-uniform hypergraphs, submitted] we extended this result to k-uniform hypergraphs for any integer . As in the 3-uniform case, the main new tool which we proved and used is an embedding lemma for k-uniform hypergraphs of bounded maximum degree into suitable k-uniform ‘quasi-random’ hypergraphs. 相似文献
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Heinrich Müller 《Discrete Mathematics》1981,34(3):319-320
Oriented hypergraphs are defined, so that it is possible to generalize propositions characterizing the chromatic number and the stability number of a graph by means of orientations and elementary paths, to the strong and weak chromatic number and the strong and weak stability number of a hypergraph. 相似文献
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三类笛卡尔积图的关联色数 总被引:2,自引:0,他引:2
图的关联色数的概念是 Brualdi和 Massey于 1 993年引入的 ,它同图的强色指数有密切的关系 .Guiduli[2 ] 说明关联色数是有向星萌度的一个特殊情况 ,迄今仅确定了某些特殊图类的关联色数 .本文给出了完全图与完全图、圈与完全图、圈与圈的笛卡尔积图的关联色数。 相似文献
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主要讨论了4一致l-超图的最小边数与最小上色数的关系,给出了上色数为3的4一致l-超图的最小边数的一个上界. 相似文献
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Let F be an r-uniform hypergraph. The chromatic threshold of the family of F-free, r-uniform hypergraphs is the infimum of all non-negative reals c such that the subfamily of F-free, r-uniform hypergraphs H with minimum degree at least \(c \left( {\begin{array}{c}|V(H)|\\ r-1\end{array}}\right) \) has bounded chromatic number. The study of chromatic thresholds of various graphs has a long history, beginning with the early work of Erd?s and Simonovits. One interesting problem, first proposed by ?uczak and Thomassé and then solved by Allen, Böttcher, Griffiths, Kohayakawa and Morris, is the characterization of graphs having zero chromatic threshold, in particular the fact that there are graphs with non-zero Turán density that have zero chromatic threshold. Here, we make progress on this problem for r-uniform hypergraphs, showing that a large class of hypergraphs have zero chromatic threshold in addition to exhibiting a family of constructions showing another large class of hypergraphs have non-zero chromatic threshold. Our construction is based on a particular product of the Bollobás–Erd?s graphs defined earlier by the authors. 相似文献