We study the random intersection graph $G_N$ constructed by these caps. We prove that for $p = \\frac{c}{N^{\\al}},\\:c >0$ and $\\al >2,$ the number of edges in graph $G_N$ follow the Poisson distribution. Also we derive the strong law results for the number of ...
题目地址:https://leetcode-cn.com/problems/remove-max-number-of-edges-to-keep-graph-fully-traversable 题目描述 Alice 和 Bob 共有一个无向图,其中包含 n 个节点和 3 种类型的边: 类型1:只能由 Alice 遍历。 类型2:只能由Bob遍历。 类型3:Alice 和Bob都可以遍历。 给你一个数组edges,其中edges[i] ...
What is the maximum possible number of edges in an n-vertex graph that does not contain a (k+1)-connected subgraph? It is easy to see that for k=1 the answer is n−1: every tree on n vertices contains n−1 edges and no 2-connected subgraphs, whereas every graph on n vertices...
Hibi, A. Mori, H. Ohsugi, A. Shikama, The number of edges of the edge polytope of a finite connected graph, arXiv:1308.3530T. Hibi, A. Mori, H. Ohsugi and A. Shikama, The number of edges of the edge polytope of a finite simple graph, Ars Math. Contem. 10(2) (2016) 323-...
Edges not in any monochromatic copy of a fixed graph When each $H_i$ is connected and non-bipartite, we introduce a variant of Ramsey number that determines the limit of $extrm{nim}(n;H_1,\\\ldots... H Liu,O Pikhurko,M Sharifzadeh 被引量: 2发表: 2017年 Counterexamples to Gerbner...
G. In this paper, we consider the function M(p, d) defined for p, d ⩾ 2 as the maximum number of edges a graph G can have when it has p vertices and the dimension of its incidence poset is at most d. It is easy to see that ...
A LOWER BOUND FOR THE NUMBER OFEDGES IN A GRAPH CONTAINING NO TWOCYCLES OF THE SAME LENGTHChunhui Lai∗Dept. of Math., Zhangzhou Teachers College,Zhangzhou, Fujian 363000, P. R. of CHINA.zjlaichu@public. zzptt. fj. cnSubmitted: November 3, 2000; Accepted: October 20, 2001.MR ...
In this paper, we study some important statistics of the random graph H (t) a,k in the Buckley–Osthus model, where t is the number of nodes, kt is the number of edges (so that ), and a>0 is the so-called initial attractiveness of a node. This model is a modification of the ...
Journal of Mathematical SciencesD.V. Karpov, An upper bound on the number of edges in an almost planar bipartite graph, J. Math. Sci. 196 (6) (2014) 737-746.D. V. Karpov. An upper bound on the number of edges in an almost planar bipartite graph. J. Math. Sci., 196(6):737-...
For an ed ge e of G; we do the following operations on G: first, delete the edge e from G; resulting the graph Ge; second, for all the vertices x of degree 3i nGe; delete x from Ge andthen completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we ...