Ad
related to: graph level structure example problems solving system of 1
Search results
Results From The WOW.Com Content Network
An example for an undirected Graph with a vertex r and its corresponding level structure For the concept in algebraic geometry, see level structure (algebraic geometry) In the mathematical subfield of graph theory a level structure of a rooted graph is a partition of the vertices into subsets that have the same distance from a given root vertex.
Graph homomorphism problem [3]: GT52 Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph. A related problem is to find a partition that is optimal terms ...
There is no single definition of a level structure; rather, depending on the space X, one introduces the notion of a level structure. The classic one is that on an elliptic curve (see #Example: an abelian scheme). There is a level structure attached to a formal group called a Drinfeld level structure, introduced in (Drinfeld 1974). [3]
A graph structure can be extended by assigning a weight to each edge of the graph. Graphs with weights, or weighted graphs, are used to represent structures in which pairwise connections have some numerical values. For example, if a graph represents a road network, the weights could represent the length of each road.
An interesting example is the graph isomorphism problem, the graph theory problem of determining whether a graph isomorphism exists between two graphs. Two graphs are isomorphic if one can be transformed into the other simply by renaming vertices. Consider these two problems: Graph Isomorphism: Is graph G 1 isomorphic to graph G 2?
The clique problem is hard for W(1), the first level of a hierarchy of hard problems from the point of view of parameterized complexity. Therefore, it is unlikely to have a fixed-parameter tractable algorithm, one whose running time takes the form O ( f ( k ) n c ) {\displaystyle O(f(k)n^{c})} for a function f {\displaystyle f} and constant c ...
The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic. An important unsolved problem in complexity theory is whether the graph isomorphism problem is in P, NP-complete, or NP-intermediate. The answer is not known, but it is believed that the problem is at least not NP-complete. [20]
A clique problem for a class of so-called M-graphs. It is shown that finding an isomorphism for n-vertex graphs is equivalent to finding an n-clique in an M-graph of size n 2. This fact is interesting because the problem of finding a clique of order (1 − ε)n in a M-graph of size n 2 is NP-complete for arbitrarily small positive ε. [43]