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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 ...
Pages in category "Computational problems in graph theory" The following 75 pages are in this category, out of 75 total. This list may not reflect recent changes .
The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment.
Pages in category "Unsolved problems in graph theory" The following 32 pages are in this category, out of 32 total. This list may not reflect recent changes. A.
When the degree is less than or equal to 2 or the diameter is less than or equal to 1, the problem becomes trivial, solved by the cycle graph and complete graph respectively. In graph theory, the degree diameter problem is the problem of finding the largest possible graph G (in terms of the size of its vertex set V) of diameter k such that the ...
The problem of constructing a solution for the graph realization problem with the additional constraint that each such solution comes with the same probability was shown to have a polynomial-time approximation scheme for the degree sequences of regular graphs by Cooper, Martin, and Greenhill. [5] The general problem is still unsolved.
Subgraph isomorphism is a generalization of the graph isomorphism problem, which asks whether G is isomorphic to H: the answer to the graph isomorphism problem is true if and only if G and H both have the same numbers of vertices and edges and the subgraph isomorphism problem for G and H is true. However the complexity-theoretic status of graph ...
If such a graph exists, it would necessarily be a locally linear graph and a strongly regular graph with parameters (99,14,1,2). The first, third, and fourth parameters encode the statement of the problem: the graph should have 99 vertices, every pair of adjacent vertices should have 1 common neighbor, and every pair of non-adjacent vertices should have 2 common neighbors.
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