共查询到20条相似文献,搜索用时 15 毫秒
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For a given positive integer t we consider graphs having maximal independent sets of precisely t distinct cardinalities and restrict our attention to those that have no vertices of degree one. In the situation when t is four or larger and the length of the shortest cycle is at least 6t ? 6, we completely characterize such graphs. 相似文献
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徐新萍 《数学的实践与认识》2009,39(10)
设G是一个图,G的部分平方图G*满足V(G*)=V(G),E(G*)=E(G)∪{uv:uv■E(G),且J(u,v)≠■},这里J(u,v)={w∈N(u)∩N(v):N(w)■N[u]∪N[v]}.利用插点方法,证明了如下结果:设G是k-连通图(k2),b是整数,0min {k,(2b-1+k)/2}(n(Y)-1),则G是哈密尔顿图.同时给出图是1-哈密尔顿的和哈密尔顿连通的相关结果. 相似文献
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Si-zhong ZHOU 《应用数学学报(英文版)》2023,39(2):232-238
A path-factor is a spanning subgraph F of G such that every component of F is a path with at least two vertices.Let k≥2 be an integer.A P≥k-factor of G means a path factor in which each component is a path with at least k vertices.A graph G is a P≥k-factor covered graph if for any e∈E(G),G has a P≥k-factor including e.Let β be a real number with 1/3≤β≤1 and k be a positive integer.We verify that(ⅰ) a k-connected graph G of order n with n≥5k+2 has a P≥3... 相似文献
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Acta Mathematicae Applicatae Sinica, English Series - A subset I of vertices of an undirected connected graph G is a nonseparating independent set (NSIS) if no two vertices of I are adjacent and G... 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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We develop a new method for enumerating independent sets of a fixed size in general graphs, and we use this method to show that a conjecture of Engbers and Galvin [7] holds for all but finitely many graphs. We also use our method to prove special cases of a conjecture of Kahn [13]. In addition, we show that our method is particularly useful for computing the number of independent sets of small sizes in general regular graphs and Moore graphs, and we argue that it can be used in many other cases when dealing with graphs that have numerous structural restrictions. 相似文献
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We consider a graph, where the nodes have a pre-described degree distribution F, and where nodes are randomly connected in accordance to their degree. Based on a recent result (R. van der Hofstad, G. Hooghiemstra
and P. Van Mieghem, “Random graphs with finite variance degrees,” Random Structures and Algorithms, vol. 17(5) pp. 76–105, 2005), we improve the approximation of the mean distance between two randomly chosen nodes given
by M. E. J. Newman, S. H. Strogatz, and D. J. Watts, “Random graphs with arbitrary degree distribution and their application,”
Physical Review. E vol. 64, 026118, pp. 1–17, 2001. Our new expression for the mean distance involves the expectation of the logarithm of the
limit of a super-critical branching process. We compare simulations of the mean distance with the results of Newman et al.
and with our new approach.
AMS 2000 Subject Classification: 05C80, 60F05 相似文献
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对强连通有向图D的一个非空顶点子集S,D中包含S的具有最少弧数的强连通有向子图称为S的Steiner子图,S的强Steiner距离d(S)等于S的Steiner子图的弧数. 如果|S|=k, 那么d(S)称为S的k-强距离. 对整数k≥2和强有向图D的顶点v,v的k-强离心率sek(v)为D中所有包含v的k个顶点的子集的k-强距离的最大值. D中顶点的最小k-强离心率称为D的k-强半径,记为sradk(D),最大k-强离心率称为D的k-强直径,记为sdiamk(D). 本文证明了,对于满足k+1≤r,d≤n的任意整数r,d,存在顶点数为n的强竞赛图T′和T″,使得sradk(T′)=r和sdiamk(T″)=d;进而给出了强定向图的k-强直径的一个上界. 相似文献
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Wayne Goddard Michael A. Henning Jeremy Lyle Justin Southey 《Annals of Combinatorics》2012,16(4):719-732
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. In this paper, we consider questions about independent domination in regular graphs. 相似文献
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Extremal problems on the number of j-independent sets in uniform simple hypergraphs are studied. Nearly optimal results on the maximum number of independent sets for the class of simple regular hypergraphs and on the minimum number of independent sets for the class of simple hypergraphs with given average degree of vertices are obtained. 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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连通图$G$的距离无符号拉普拉斯矩阵定义为$\mathcal{Q}(G)=Tr(G)+D(G)$, 其中$Tr(G)$和$D(G)$分别为连通图$G$的点传输矩阵和距离矩阵. 图$G$的距离无符号拉普拉斯矩阵的最大特征值称为$G$的距离无符号拉普拉斯谱半径. 本文确定了给定点数的双圈图中具有最大的距离无符号拉普拉斯谱半径的图. 相似文献
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In this paper we investigate the Erdos/Falconer distance conjecture for a natural class of sets statistically, though not
necessarily arithmetically, similar to a lattice. We prove a good upper bound for spherical means that have been classically
used to study this problem. We conjecture that a majorant for the spherical means suffices to prove the distance conjecture(s)
in this setting. For a class of non-Euclidean distances, we show that this generally cannot be achieved, at least in dimension
two, by considering integer point distributions on convex curves and surfaces. In higher dimensions, we link this problem
to the question about the existence of smooth well-curved hypersurfaces that support many integer points. 相似文献