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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 ...
The Petersen graph (on the left) and its complement graph (on the right).. In the mathematical field of graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices of H are adjacent if and only if they are not adjacent in G.
Inverse proportionality with product x y = 1 . Two variables are inversely proportional (also called varying inversely, in inverse variation, in inverse proportion) [2] if each of the variables is directly proportional to the multiplicative inverse (reciprocal) of the other, or equivalently if their product is a constant. [3]
Here is the graph for these two equations. For the numeric values involved in the problem statement, these graphs are "similar" and it is easy to see why individuals consider their incorrect answers perfectly reasonable. Now consider our inverse proportion using the "water triangle".
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.
Fixed point logics, and extensions of these logics that also allow integer counting variables whose values range from 0 to the number of vertices, have been used in descriptive complexity in an attempt to provide a logical description of decision problems in graph theory that can be decided in polynomial time. The fixed point of a logical ...
The independent set problem and the clique problem are complementary: a clique in G is an independent set in the complement graph of G and vice versa. Therefore, many computational results may be applied equally well to either problem. For example, the results related to the clique problem have the following corollaries:
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
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