This article provides sharp bounds for the maximum number of edges possible in a simple graph with restricted values of two of the three parameters, namely, maxi- mum matching size, independence number and maximum degree. We also construct extremal graphs that achieve the edge bounds in all ...
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....
摘要: 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).关键词:length raised integer
An exact formula is given for the maximum number of edges in a graph that admits a three-dimensional grid-drawing contained in a given bounding box. The first universal lower bound on the volume of threedimensional grid-drawings is obtained as a corollary. Our results generalise to the setting...
A DAG is given to us, we need to find maximum number of edges that can be added to this DAG, after which new graph still remain a DAG that means the reformed graph should have maximal number of edges, adding even single edge will create a cycle in graph. ...
A topological graph is called k -quasi-planar if it does not contain k pairwise crossing edges. It is conjectured that for every fixed k, the maximum number of edges in a k-quasi-planar graph on n vertices is O(n). We provide an affirmative answer to the case k=4. 机译:如果拓...
The Maximum Induced Matching (MIM) Problem asks for a largest set of pairwise vertex-disjoint edges in a graph which are pairwise of distance at least two... Andreas Brandstaedt,Chinh T. Hoang - 《Algorithmica》 被引量: 35发表: 2008年 A simple linear time algorithm for finding a maximu...
作者: A Arman 摘要: In this thesis a problem of determining the maximum number of cycles for the following classes of graphs is considered: triangle-free graphs; K_r-free graphs; graphs with m edges; graphs with n vertices and m edges; multigraphs with m edges and multigraphs with n ve...
in a graph that are all connected to one another. Take a look at the simple graph inFigure 1. The graph has nine nodes and 13 edges. The graph is unweighted (there are no priorities associated with the edges) and undirected (all edges are bidirectional). Nodes 2, 4 and 5 ...
The problem studied in this paper is that of finding the maximum number of Hamiltonian cycles in a graph with a given number of vertices and edges. The main results are a lower bound and an upper bound, both given by closed-form formulas, for the maximum number of Hamiltonian cycles in ...