In 1975, Erds raised the following problem: Let f(n) be the maximum possible number of edges in a graph on n vertices in which there are no two cycles having the same length. Determine f(n).施永兵中国科学通报:英文版Y. Shi, The number of edges in a maximum graphs with uni-length ...
Firstly, there should be at most one edge from a specific vertex to another vertex. This ensures all the vertices are connected and hence the graph contains the maximum number of edges. In short, a directed graph needs to be a complete graph in order to contain the maximum number of edges...
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 ...
We want to derive a linear in (n−k) bound on the number of edges in a graph that does not contain (k+1)-connected subgraphs. But the bound becomes linear only for graphs with large number of vertices; while for small graphs the dependency is quadratic in n−k. The main difficult...
in G. This poset is called the incidence poset of 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....
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 ...
It is known that the number of edges of the edge polytope of the complete graph with $d$ vertices is $d(d-1)(d-2)/2$. In this paper, we study the maximum possible number $\\mu_d$ of edges of the edge polytope arising from finite simple graphs with $d$ vertices. We show ...
We characterize the complete quality-of-service (QoS) feasibility region and present a simple feasibility test for given QoS requirements in the Gaussian v... R Hunger,M Joham - 《IEEE Transactions on Signal Processing》 被引量: 75发表: 2010年 The maximum number of edges in a graph of bou...
The limit behavior of Markov chains with discrete time and a finite number of states (MCDT) depending on the number n of itssteps has been almost completel... V.,V.,Chichagov - 《Journal of Mathematical Sciences》 被引量: 2发表: 1995年 Number of edges in inhomogeneous random graphs We...
properly connected if any two vertices are connected by a path whose edges are properly coloured. The. proper connection number of a connected graph. G, denoted by. pc(G), is the smallest number of colours that are needed in order to make. G properly connected. Our main result is the ...