共查询到19条相似文献,搜索用时 62 毫秒
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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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一、 引言 本文中未加说明的图论术语来自文献[1]。图G=(V,E)称为弦图,如果G的任何长度大于3的圈都有弦,或者等价地,任何长度大于3的圈都不会是G的点导出子图。本文中,子图总是指点导出子图,点子集S导出的G的子图记为G[S]。团是指完备子图,通常用它的点集来表示。如果图G的每个点v都带有点权w(v),则点子集S的权定义为S中点的权的和。 相似文献
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如果对一个简单图G的每一个与G的顶点数同奇偶的独立集I,都有G-I有完美匹配,则称G是独立集可削去的因子临界图.如果图G不是独立集可削去的因子临界图,而对任意两个小相邻的顶点x与y,G xy足独立集可削去的因子临界图,则称G足极大非独立集可削去的因子临界图,本刻画了极大非独立集可削去的因子临界图。 相似文献
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关于哈密尔顿连通图的一个基本结果是Ore给出的:设G是n阶图,若对于任意两个不相邻顶点u和v,有d(u) d(v)≥n 1,则G是哈密尔顿连通的.设G是一个图,对于任意u (?)V(G),令N(U)=∪_(u∈∪)N(u),d(U)=|N(U)|,称d(U)是U的度.本文利用独立集的度和得到如下结果:设s和t是正整数,G是(2s 2t 1)-连通n阶图.若对于任两个强不交独立集S,T,|S|=s,|T|=t,有d(S) d(T)≥n 1.则G是哈密尔顿连通的.同时也得到图的哈密尔顿性的其它相关结果.两个独立集S和T称为强不交的,如果S∪T也是独立集. 相似文献
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部分控制集问题是对于给定的顶点赋权图G=(V,E;c)和正整数K,寻找图G一个顶点子集T,使得在其控制下的顶点个数不小于K且T中顶点权和达到最小。本文讨论了部分控制集问题的NP-困难性;给出了该问题的一种修正Greedy近似算法,并对其近似度H(K)给出了证明。 相似文献
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设α(G)表示简单图G=(V,E)的独立数.本文给出了α(G)的一个新的下界:α(G)≥∑v∈V(λd(v)+1)/(d(v)+λd(v)+1),其中λd(v)=max{0,βN(v)-d(v)},d(v)=|N(v)|,N(v)={w∈V|(v,w)∈E},βN(v)=minw∈N(v)d(w). 相似文献
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可变抽样区间的单边控制图 总被引:4,自引:0,他引:4
利用质量控制图监督生产过程时 ,通常每隔固定时间从过程抽取固定容量的样本。本文在前文[1] 的基础上设计具有可变抽样区间的单边标准差 (S)图、极差 (R)图和不合格品数 (np)图。计算了这三个图发信号前的平均样本数和平均时间 ,并同固定抽样区间的常规控制图作比较。所设计的控制图能缩短过程失控时间从而减少不合格品数。 相似文献
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Three formulations for the Minimum 2-Connected Dominating Set Problem, valid inequalities, a primal heuristic and Branch-and-Cut algorithms are introduced in this paper. As shown here, the preliminary computational results so far obtained indicate that these algorithms are quite promising. 相似文献
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We describe small dominating sets of the incidence graphs of finite projective planes by establishing a stability result that shows that dominating sets are strongly related to blocking and covering sets. Our main result states that if a dominating set in a projective plane of order is smaller than (i.e., twice the size of a Baer subplane), then it contains either all but possibly one points of a line or all but possibly one lines through a point. Furthermore, we completely characterize dominating sets of size at most . In Desarguesian planes, we could rely on strong stability results on blocking sets to show that if a dominating set is sufficiently smaller than 3q, then it consists of the union of a blocking set and a covering set apart from a few points and lines. 相似文献
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We present two heuristics for finding a small power dominating set of cubic graphs. We analyze the performance of these heuristics on random cubic graphs using differential equations. In this way, we prove that the proportion of vertices in a minimum power dominating set of a random cubic graph is asymptotically almost surely at most 0.067801. We also provide a corresponding lower bound of using known results on bisection width. 相似文献
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Zoltán Lóránt Nagy 《Journal of Graph Theory》2017,84(4):566-580
We study the existence and the number of k‐dominating independent sets in certain graph families. While the case namely the case of maximal independent sets—which is originated from Erd?s and Moser—is widely investigated, much less is known in general. In this paper we settle the question for trees and prove that the maximum number of k‐dominating independent sets in n‐vertex graphs is between and if , moreover the maximum number of 2‐dominating independent sets in n‐vertex graphs is between and . Graph constructions containing a large number of k‐dominating independent sets are coming from product graphs, complete bipartite graphs, and finite geometries. The product graph construction is associated with the number of certain Maximum Distance Separable (MDS) codes. 相似文献
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A graph is uniquely hamiltonian if it contains exactly one hamiltonian cycle. In this note we prove that there are no r‐regular uniquely hamiltonian graphs when r > 22. This improves upon earlier results of Thomassen. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 233–244, 2007 相似文献
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Galvin showed that for all fixed δ and sufficiently large n, the n‐vertex graph with minimum degree δ that admits the most independent sets is the complete bipartite graph . He conjectured that except perhaps for some small values of t, the same graph yields the maximum count of independent sets of size t for each possible t. Evidence for this conjecture was recently provided by Alexander, Cutler, and Mink, who showed that for all triples with , no n‐vertex bipartite graph with minimum degree δ admits more independent sets of size t than . Here, we make further progress. We show that for all triples with and , no n‐vertex graph with minimum degree δ admits more independent sets of size t than , and we obtain the same conclusion for and . Our proofs lead us naturally to the study of an interesting family of critical graphs, namely those of minimum degree δ whose minimum degree drops on deletion of an edge or a vertex. 相似文献
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Hans-Gert Gräbe 《Journal of Algebraic Combinatorics》1993,2(2):137-145
In the first part we generalize the notion of strongly independent sets, introduced in [10] for polynomial ideals, to submodules of free modules and explain their computational relevance. We discuss also two algorithms to compute strongly independent sets that rest on the primary decomposition of squarefree monomial ideals.Usually the initial ideal in(I) of a polynomial ideal I is worse than I. In [9] the authors observed that nevertheless in(I) is not as bad as one should expect, showing that in(I) is connected in codimension one if I is prime.In the second part of the paper we add more evidence to that observation. We show that in(I) inherits (radically) unmixedness, connectedness in codimension one and connectedness outside a finite set of points from I and prove the same results also for initial submodules of free modules. The proofs use a deformation from I to in(I ). 相似文献
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Martin Farber 《Operations Research Letters》1982,1(4):134-138
A graph chordal if it does not contain any cycle of length greater than three as an induced subgraph. A set of S of vertices of a graph G = (V,E) is independent if not two vertices in S are adjacent, and is dominating if every vertex in V?S is adjacent to some vertex in S. We present a linear algorithm to locate a minimum weight independent dominating set in a chordal graph with 0–1 vertex weights. 相似文献