共查询到20条相似文献,搜索用时 78 毫秒
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设H=(V,E)是以V为顶点集, E为(超)边集的超图. 如果H的每条边均含有k个顶点, 则称H是k-一致超图. 超图H的点子集T称为它的一个横贯, 如果T 与H 的每条边均相交. 超图H的全横贯是指它的一个横贯T, 并且T还满足如下性质: T中每个顶点均至少有一个邻点在T中. H 的全横贯数定义为H 的最小全横贯所含顶点的数目, 记作\tau_{t}(H). 对于整数k\geq 2, 令b_{k}=\sup_{H\in{\mathscr{H}}_{k}}\frac{\tau_{t}(H)}{n_{H}+m_{H}}, 其中n_H=|V|, m_H=|E|, {\mathscr{H}}_{k} 表示无孤立点和孤立边以及多重边的k-一致超图类. 最近, Bujt\'as和Henning等证明了如下结果: b_{2}=\frac{2}{5}, b_{3}=\frac{1}{3}, b_{4}=\frac{2}{7}; 当k\geq 5 时, 有b_{k}\leq \frac{2}{7}以及b_{6}\leq \frac{1}{4}; 当k\geq 7 时, b_{k}\leq \frac{2}{9}. 证明了对5-一致超图, b_{5}\leq \frac{4}{15}, 从而改进了当k=5 时b_k的上界. 相似文献
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《应用数学与计算数学学报》2015,(4)
设G为简单图,若G的点子集S与图中的每个团都有非空的交,则称S是图G的一个团横贯集,这里G的团是指图中的极大完全子图且至少包含两个点.图G的最小团横贯集所含点的数目称为G的团横贯数,记作τC(G).如果G的每条边至少包含在一个t阶完全子图中且τC(G)≤|V(G)|/t,则称G具有〈t〉一性质.提出了平面图分离4-团的概念.首先证明了最大度不超过5的平面图具有〈t〉-性质.其次,对任意平面图G,若它不含分离4-团且每条边都包含在一个4-团之中,得到了它的横贯数的上界和独立数的可达下界. 相似文献
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图$G(V,E)$的全色数 $\chi_{t}(G)$就是将$V\bigcup E$分成彼此不相交的全独立分割集的最小个数。 如果任何两个$V\bigcup E$的全独立分割集的元素数目相差不超过1,那么 $V \bigcup E$的全独立分割集的最小个数就称为图$G$的均匀全色数,记为$\chi_{et}(G)$。 在本文中我们给出了当 $m \geq n \geq 3$ 时 $W_m\bigvee K_n$,$F_m \bigvee K_n$及$S_m \bigvee K_n$ 的均匀全色数. 相似文献
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对于简单图G=(V,E),顶点子集F■V,如果由V\F导出的子图G′= (V\F,E′)是不含圈的,则称F是图G的一个反馈点集.点数最少的反馈点集称图的最小反馈点集,最小的点数称为反馈数.文章给出了交叉立方体网络的一个等价定义,用递归的方法构造出交叉立方体网络的诱导树,证明了诱导树的阶数Fibonacci数,进而得到叉立方体网络反馈数的上下界. 相似文献
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A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G.The clique-transversal number,denoted Tc(G),is the minimum cardinality of a clique- transversal set in G.In this paper we present the bounds on the clique-transversal number for regular graphs and characterize the extremal graphs achieving the lower bound.Also,we give the sharp bounds on the clique-transversal number for claw-free cubic graphs and we characterize the extremal graphs achieving the lower bound. 相似文献
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In this paper, a new
zero-divisor graph $\overline{\G}(S)$ is defined and studied for a
commutative semigroup $S$ with zero element. The properties and
the structure of the graph are studied; for any complete graph and
complete bipartite graph $G$, commutative semigroups $S$ are
constructed such that the graph $G$ is isomorphic to
$\overline{\G}(S)$. 相似文献
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Let G be a simple graph. A total coloring f of G is called 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 E-total-coloring f of a graph G and any vertex u of G, let Cf (u) or C(u) denote the set of colors of vertex u and the edges incident to u. We call C(u) the color set of u. 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 colorings of G is denoted by X^evt(G), and it is called the VDET chromatic number of G. In this article, we will discuss vertex-distinguishing E-total colorings of the graphs mC3 and mC4. 相似文献
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给定一个赋权图$G=(V,E;w,c)$以及图$G$的一个支撑子图$G_{1}=(V,E_{1})$,这里源点集合$S=\{s_{1},s_{2},\cdots,s_{k}\}\subseteq V$,权重函数$w:E\rightarrow\mathbb{R}^{+}$,费用函数$c:E\setminus E_{1}\rightarrow\mathbb{Z}^{+}$和一个正整数$B$,本文考虑两类限制性多源点偏心距增广问题,具体叙述如下:(1)限制性多源点最小偏心距增广问题是要寻找一个边子集$E_{2}\subseteq E\setminus E_{1}$,满足约束条件$c(E_{2})$$\leq$$B$,目标是使得子图$G_{1}\cup E_{2}$上源点集$S$中顶点偏心距的最小值达到最小;(2)限制性多源点最大偏心距增广问题是要寻找一个边子集$E_{2}\subseteq E\setminus E_{1}$,满足约束条件$c(E_{2})$$\leq$$B$,目标是使得子图$G_{1}\cup E_{2}$上源点集$S$中顶点偏心距的最大值达到最小。本文设计了两个固定参数可解的常数近似算法来分别对上述两类问题进行求解。 相似文献
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给定一个赋权图$G=(V,E;w,c)$以及图$G$的一个支撑子图$G_{1}=(V,E_{1})$,这里源点集合$S=\{s_{1},s_{2},\cdots,s_{k}\}\subseteq V$,权重函数$w:E\rightarrow\mathbb{R}^{+}$,费用函数$c:E\setminus E_{1}\rightarrow\mathbb{Z}^{+}$和一个正整数$B$,本文考虑两类限制性多源点偏心距增广问题,具体叙述如下:(1)限制性多源点最小偏心距增广问题是要寻找一个边子集$E_{2}\subseteq E\setminus E_{1}$,满足约束条件$c(E_{2})$$\leq$$B$,目标是使得子图$G_{1}\cup E_{2}$上源点集$S$中顶点偏心距的最小值达到最小;(2)限制性多源点最大偏心距增广问题是要寻找一个边子集$E_{2}\subseteq E\setminus E_{1}$,满足约束条件$c(E_{2})$$\leq$$B$,目标是使得子图$G_{1}\cup E_{2}$上源点集$S$中顶点偏心距的最大值达到最小。本文设计了两个固定参数可解的常数近似算法来分别对上述两类问题进行求解。 相似文献
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Let G be a simple graph.An IE-total coloring f of G refers to a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color.Let C(u) be the set of colors of vertex u and edges incident to u under f.For an IE-total coloring f of G using k colors,if C(u)=C(v) for any two different vertices u and v of V(G),then f is called a k-vertex-distinguishing IE-total-coloring of G,or a k-VDIET coloring of G for short.The minimum number of colors required for a VDIET coloring of G is denoted by χ ie vt (G),and it is called the VDIET chromatic number of G.We will give VDIET chromatic numbers for complete bipartite graph K4,n (n≥4),K n,n (5≤ n ≤ 21) in this article. 相似文献
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Abstract Let Kv be the complete graph on v vertices, and G a finite simple undirected graph without isolated vertices. A G-packing of Kv, denoted by (v, G, 1)-packing, is a pair (X,A) where X is the vertex set of K+ and +4 is a family of edge-disjoint subgraphs isomorphic to G in Kv. In this paper, the maximum number of subgraphs in a (v, G, 1)-packing is determined when G is K2 x K3, the Cartesian product of K2 and K3, leaving two orders undetermined. This design originated from the use of DNA library screening. 相似文献
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A set D of vertices in a graph G = (V, E) is a locating-dominating set (LDS) if for every two vertices u, v of V / D the sets N(u) ∩D and N(v) ∩ D are non-empty and different. The locating-domination number γL(G) is the minimum cardinality of an LDS of G, and the upper-locating domination number FL(G) is the maximum cardinality of a minimal LDS of G. In the present paper, methods for determining the exact values of the upper locating-domination numbers of cycles are provided. 相似文献