Примеры использования Number of edges на Английском языке и их переводы на Русский язык
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The number of edges is g/pr.
In particular, if r is odd then the number of edges must be divisible by r.
The number of edges in a crown graph is the pronic number nn- 1.
The degree of the polynomial equals the number of edges in the corresponding tree.
Thus the number of edges is 2 less than the sum of the numbers of vertices and faces.
An even tighter bound is possible when the number of edges is strictly greater than n2/4.
If the number of edges meeting at a vertex is uniformly bounded, and the potential is bounded, then H is bounded and self-adjoint.
John Hopcroft andRobert Tarjan derived a means of testing the planarity of a graph in time linear to the number of edges.
Then by the above the number of edges of G is greater than the number of vertices, hence|G′|>|G|.
A maximum matching(also known as maximum-cardinality matching)is a matching that contains the largest possible number of edges.
Therefore, H does not obey property(∗),which requires that this total number of edges(deg v1+ deg vn) be greater than or equal to n.
In any bipartite graph, the number of edges in a maximum matching equals the number of vertices in a minimum vertex cover.
The complexity M is then defined asM E- N+ 2P, where E the number of edges of the graph.
The number of edges in a spanning forest of a graph with[math]n[/math] vertices consisting of[math]c[/math] connected components is[math]n-c/math.
Some authors prefer to use the number of vertices or the number of edges as the size measure in the context of graph problems.
Note that it makes a difference whether the algorithm is allowed to be sub-exponential in thesize of the instance, the number of vertices, or the number of edges.
One wants a subset S of the vertex set such that the number of edges between S and the complementary subset is as large as possible.
It is possible to construct an optimal layout in time O(m log log n), where n denotes the number of vertices of the input graph andm denotes the number of edges.
The Erdős-Stone theorem extends Turán's theorem by bounding the number of edges in a graph that does not have a fixed Turán graph as a subgraph.
The Euler characteristic states that for any convex polyhedron, the number of faces plusthe number of vertices(corners) equals the number of edges plus two.
The number of vertices in Cn equals the number of edges, and every vertex has degree 2; that is, every vertex has exactly two edges incident with it.
On the other hand,if every vertex has at most two neighbors, then by the handshaking lemma the number of edges is at most the number of vertices.
Up to constant factors, z(n; t)also bounds the number of edges in an n-vertex graph(not required to be bipartite) that has no Kt, t subgraph.
However, no polynomial-time algorithm is known for finding a minimum maximal matching, that is,a maximal matching that contains the smallest possible number of edges.
In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path(also called a graph geodesic) connecting them.
This work concerns the number of edges in biclique-free bipartite graphs, but a standard application of the probabilistic method transfers the same bound to arbitrary graphs.
For any graph H, the simple H-minor-free graphs must be sparse,which means that the number of edges is less than some constant multiple of the number of vertices.
These bounds generalize Turán's theorem on the number of edges in a triangle-free graph, and they are the best possible bounds for this problem,in that for any smaller number of edges there exist graphs that do not contain a k{\displaystyle k}-fan.
In a bipartite graph with no isolated vertices,the number of vertices in a maximum independent set equals the number of edges in a minimum edge covering; this is Kőnig's theorem.
Kőnig's theorem states that,in any bipartite graph, the number of edges in a maximum matching is equal to the number of vertices in a minimum vertex cover.