>= (t + 1)n - t- t - 3 (n >= 3t). Furthermore, the results are sharp.doi:10.1016/S0012-365X(97)00078-2Ralph J. FaudreeJ. SheehanDiscrete MathematicsR. J. Faudree and J. Sheehan.The maximum number of edges in a graph with fixed edge-degree. Discrete Mathematics . 1998...
In this tutorial, we’ll discuss how to calculate the maximum number of edges in a directed graph. 2. A Simple Definition of Directed Graph In graph theory, graphs can be categorized generally as a directed or an undirected graph. In this section, we’ll focus our discussion on a directed...
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....
In the context of maximum flow, the edges in a graph are considered to have acapacityas represented by the edge weight. The capacity of an edge is the amount of flow that can pass through that edge. Therefore, the maximum flow between two nodes in a graph maximizes the amount of flow ...
Acliqueis a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for the following graph classes: (1) graphs withnvertices andmedges; (2) graphs withnvertices,medges, and maximum degree Δ; (3)d-degenerate graphs withnvertices andmedges;...
We prove the conjecture for connected graphs with ( G )4, with the additional restriction that m 2 n -1, where n is the number of vertices and m is the number of edges in G . Note that for any graph G , m 2 n , when ( G )4. It follows that for any graph G if ( G )...
The maximum flow between vertices v_i and v_j in a graph G is exactly the weight of the smallest set of edges to disconnect G with v_i and v_j in different components (Ford and Fulkerson 1962; Skiena 1990, p. 178).
18 April 2022 © The Author(s) 2022 Abstract Maximum biclique search, which finds the biclique with the maximum number of edges in a bipartite graph, is a fundamental problem with a wide spectrum of applications in different domains, such as E-Commerce, social analysis, web services, and ...
is to find a minimum set of edges whose removal separates each pair (s k , t k ) in an augmented grid (i.e. where each terminal vertex is linked to the graph by a unique edge, e.g. [7]). There exists a duality relationship between the continuous relaxations of linear formulation...
We let ST=⋂x∈TN(x) and define a new graph by converting T∪ST into a clique (of size r+1) and deleting all the edges [ST,V(G)∖(T∪S)]. In other words we defineGT=G+(ST2)−[ST,V(G)∖(T∪ST)], where (ST2) is the set of all pairs in ST and, for sets ...