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A circle with five chords and the corresponding circle graph. In graph theory, a circle graph is the intersection graph of a chord diagram.That is, it is an undirected graph whose vertices can be associated with a finite system of chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other.
The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP ...
Bivariegated graph; Cage (graph theory) Cayley graph; Circle graph; Clique graph; Cograph; Common graph; Complement of a graph; Complete graph; Cubic graph; Cycle graph; De Bruijn graph; Dense graph; Dipole graph; Directed acyclic graph; Directed graph; Distance regular graph; Distance-transitive graph; Edge-transitive graph; Interval graph ...
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 ...
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.
In the mathematical discipline of graph theory, a polygon-circle graph is an intersection graph of a set of convex polygons all of whose vertices lie on a common circle. These graphs have also been called spider graphs. This class of graphs was first suggested by Michael Fellows in 1988, motivated by the fact that it is closed under edge ...
This is a list of Wikipedia articles about curves used in different fields: mathematics ... Circle. Unit circle; Ellipse; Parabola; Hyperbola. Unit hyperbola; Degree 3.
If a circular-arc graph G has an arc model that leaves some point of the circle uncovered, the circle can be cut at that point and stretched to a line, which results in an interval representation. Unlike interval graphs, however, circular-arc graphs are not always perfect, as the odd chordless cycles C 5, C 7, etc., are circular-arc graphs.
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