共查询到20条相似文献,搜索用时 62 毫秒
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本文证明了若G是连通、局部连通的无爪图,则G是泛连通图的充要条件为G是3-连通图.这意味着H.J.Broersma和H.J.Veldman猜想成立. 相似文献
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6连通图中的可收缩边 总被引:4,自引:0,他引:4
Kriesell(2001年)猜想:如果κ连通图中任意两个相邻顶点的度的和至少是2[5κ/4]-1则图中有κ-可收缩边.本文证明每一个收缩临界6连通图中有两个相邻的度为6的顶点,由此推出该猜想对κ=6成立。 相似文献
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高度图的独立集复形 总被引:3,自引:0,他引:3
给定图G,称以G的所有独立集为单形的抽象复形I(G)为G的独立集复形.如果两个图G和H的独立集复形I(G)和I(H)的各阶同调群都是同构的,则称两个图是独立同调的.J(G)表示Gc的连通分支数,J3K2(G)表示Gc中同构于(3H2)c的连通分支数.本文研究了最小次δ(G)至少为其阶数|V(G)|减5的图G的独立集复形的结构,对满足δ(G)≥|V(C)|5,δ(H)≥|V(H)|-5的两个图G和H,(I)证明了,G和H独立同调的充要条件为J(G)=J(H),J3K2(G)=J3K2(H),且I(G)和I(H)的Euler示性数相同.(Ⅱ)给出了一个在图上计算I(G)的一维Betti数的方法,得到了一个I(G)是无圈复形的充要条件 相似文献
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Let G be a3-connected graph with n vertices.The paper proves that if for each pair of verti-ces u and v of G,d(u,v)=2,has|N(u)∩N(v)|≤α(αis the minimum independent set num-ber),and then max{d(u),d(v)|≥n 1/2,then G is a Hamilton connected graph. 相似文献
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G是一个k-连通图,T是G的一个k-点割,若G-T可被划分成两个子图G1,G2,且|G1 |≥2,|G2 |≥2,则称T是G的一个非平凡点割.假定G是一个不含非平凡(k-1)点割的(k-1)-连通图,则称G是一个拟k-连通图.证明了对任意一个k≥5且t>k/2的整数,若G是一个不含(K2+tK1)的k-连通图,且G中任... 相似文献
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In the last 50 years, Graph theory has seen an explosive growth due to interaction with areas like computer science, electrical and communication engineering, Operations Research etc. Perhaps the fastest growing area within graph theory is the study of domination, the reason being its many and varied applications in such fields as social sciences, communication networks, algorithm designs, computational complexity etc. Henda C. Swart has rightly commented that the theory of domination in graphs is like a ‘growth industry’. There are several types of domination depending upon the nature of domination and the nature of the dominating set. In the following, we present weakly connected domination in connected graphs. 相似文献
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设G是n阶连通图.γ_c(G),d_c(G),i(G)和ir(G)分别表示G图的连通Domination数,连通Domatic数,独立Domination数和Irredundance数,k(G)表示G的连通度.本文证明了下列结论. (1) 如n≥3,则i(G) γ_c(G)≤n [n/3]-2; (2) γ_c(G)≤4ir(G)-2; (3) γ_c(G)≤k(G) 1; (4) 如G≠K_n,则d_c(G)≤k(G). 此外,本文给出了满足等式γ_c(G) γ_c(G)=n和γ_c(G) γ_c(G)=n 1的图G的一个特征. 相似文献
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《Quaestiones Mathematicae》2013,36(6):841-848
AbstractA set S of vertices in a graph G is a connected dominating set of G if S dominates G and the subgraph induced by S is connected. We study the graphs for which adding any edge does not change the connected domination number. 相似文献
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具有最大控制数的连通图的刻画 总被引:3,自引:3,他引:0
设G为一个P阶图,γ(G)表示G的控制数.显然γ(G)≤[p/2].本文的目的是刻画达到这个上界的连通图.主要结果:(1)当p为偶数时,γ(G)=p/2当且仅当G≈C4或者G为某连通图的冠;(2)当p为奇数时,γ(G)=(p-1)/2当且仅当G的每棵生成树为定理3.1中所示的两类树之一. 相似文献
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Let \({F_1, F_2, \ldots, F_k}\) be graphs with the same vertex set V. A subset \({S \subseteq V}\) is a simultaneous dominating set if for every i, 1 ≤ i ≤ k, every vertex of F i not in S is adjacent to a vertex in S in F i ; that is, the set S is simultaneously a dominating set in each graph F i . The cardinality of a smallest such set is the simultaneous domination number. We present general upper bounds on the simultaneous domination number. We investigate bounds in special cases, including the cases when the factors, F i , are r-regular or the disjoint union of copies of K r . Further we study the case when each factor is a cycle. 相似文献
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关于图的减控制与符号控制 总被引:18,自引:2,他引:18
给定一个图G=(V,E),一个函数f:V→{-1,0,1}被称为G的减控制函数,如果对任意v∈V(G)均有∑μ∈N[v]f(μ)≥1。G的减控制数定义为γ-(G)=min{∑v∈Vf(v)|f是G的减控制函数}。图G的符号控制函数的正如减控制函数,差别是广{-1,0,1}换成{-1,1}。符号控制数γs(G)是类似的。本文获得γ-G)和γs(G)的一些下界。同时也证明并推广了 Jean Dunbar等提出的一个猜想,即对任意 n阶 2部图 G,均有γ-(G)≥ 4(n+11/2-1)-n成立。 相似文献
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Paul Dorbec Michael A. Henning Mickael Montassier Justin Southey 《Journal of Graph Theory》2015,80(4):329-349
A set S of vertices in a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S. The independent domination number of G, denoted by , is the minimum cardinality of an independent dominating set. In this article, we show that if is a connected cubic graph of order n that does not have a subgraph isomorphic to K2, 3, then . As a consequence of our main result, we deduce Reed's important result [Combin Probab Comput 5 (1996), 277–295] that if G is a cubic graph of order n, then , where denotes the domination number of G. 相似文献
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We study the complexity of INDEPENDENT DOMINATION, a well-known algorithmical problem, for triangle graphs, i.e., graphs G satisfying the following triangle condition: for every maximal independent set I in G and every edge uv in , there is a vertex such that induces a triangle in G. We show that INDEPENDENT DOMINATION within triangle graphs is closely connected with the general STABLE MAX-CUT problem. However, the INDEPENDENT DOMINATION problem is NP-complete for K1,4-free triangle graphs. Finally, we investigate some natural invariants related to independent domination from the algorithmical point of view and apply our results to triangle graphs. 相似文献
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We present results on total domination in a partitioned graph G = (V, E). Let γ
t
(G) denote the total dominating number of G. For a partition , k ≥ 2, of V, let γ
t
(G; V
i
) be the cardinality of a smallest subset of V such that every vertex of V
i
has a neighbour in it and define the following
We summarize known bounds on γ
t
(G) and for graphs with all degrees at least δ we derive the following bounds for f
t
(G; k) and g
t
(G; k).
相似文献
(i) | For δ ≥ 2 and k ≥ 3 we prove f t (G; k) ≤ 11|V|/7 and this inequality is best possible. |
(ii) | for δ ≥ 3 we prove that f t (G; 2) ≤ (5/4 − 1/372)|V|. That inequality may not be best possible, but we conjecture that f t (G; 2) ≤ 7|V|/6 is. |
(iii) | for δ ≥ 3 we prove f t (G; k) ≤ 3|V|/2 and this inequality is best possible. |
(iv) | for δ ≥ 3 the inequality g t (G; k) ≤ 3|V|/4 holds and is best possible. |