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1. Perfect graph theorem: In graph theory, the perfect graph theorem of László Lovász (1972a, 1972b) states that an undirected graph is perfect if and only if its complement graph is also perfect. This result had been conjectured by Berge (1961, 1963), and it is ... (An undirected graph is perfect if and only if its complement graph is also perfect) [100%] 2023-09-16 [Theorems in graph theory] [Articles containing proofs]...
2. Closed-graph theorem: Let $X$ and $Y$ be complete metric linear spaces with translation-invariant metrics, i.e. $\rho_X(x_1+a,x_2+a) = \rho_X(x_1,x_2)$, $x_1,x_2,a \in X$ (similarly for $Y$), and let $T$ be a linear operator from $X ... (Mathematics) [100%] 2023-09-28
3. Closed graph theorem: In mathematics, the closed graph theorem may refer to one of several basic results characterizing continuous functions in terms of their graphs. Each gives conditions when functions with closed graphs are necessarily continuous. (Theorem relating continuity to graphs) [100%] 2024-02-07 [Theorems in functional analysis]
4. Borel graph theorem: In functional analysis, the Borel graph theorem is generalization of the closed graph theorem that was proven by L. Schwartz. [100%] 2024-04-12 [Theorems in functional analysis]
5. Graph theory: A branch of discrete mathematics, distinguished by its geometric approach to the study of various objects. The principal object of the theory is a graph and its generalizations. (Mathematics) [99%] 2023-11-06 [Graph theory]
6. Graph theory: In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges ... (Area of discrete mathematics) [99%] 2023-12-19 [Graph theory]
7. Graph theory: Graph theory is the field of mathematics which deals with the study of graphs. A graph is defined as a set of vertices or nodes and edges or arcs which join the nodes. [99%] 2023-07-05
8. Graph theory: In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges ... (Area of discrete mathematics) [99%] 2024-08-24 [Graph theory]
9. Theorem: A theorem is a statement that can be proven via logic which generally stems from a collection of postulates or axioms. They have been in use since Euclidean geometry as the basis of geometrical facts. [96%] 2023-02-21 [Mathematics]
10. Theorem: In logic, a theorem is formally meant to be a formula that can be transformed by applying inferential rules to axioms in a deductive system. This formal notion of proofs in logic is crucial in fields such as proof theory ... [96%] 2023-02-03
11. Theorem: In mathematics, a theorem is a statement that has been proved, or can be proved. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a ... (In mathematics, a statement that has been proved) [96%] 2023-09-23 [Theorems] [Logical consequence]...
12. Theorem: A mathematical statement whose truth has been established by means of a proof. The concept of a theorem developed and became more precise together with the concept of a mathematical proof. (Mathematics) [96%] 2023-10-18
13. Pearls in Graph Theory: Pearls in Graph Theory: A Comprehensive Introduction is an undergraduate-level textbook on graph theory by Nora Hartsfield and Gerhard Ringel. It was published in 1990 by Academic Press with a revised edition in 1994 and a paperback reprint of ... (1990 book by Gerhard Ringel and Nora Hartsfield) [90%] 2024-08-28 [Graph theory] [Mathematics textbooks]...
14. Theorum: Theorum (rhymes with decorum, apparently) is a neologism proposed by Richard Dawkins in The Greatest Show on Earth to distinguish the scientific meaning of theory from the colloquial meaning. In most of the opening introduction to the show, he substitutes ... [87%] 2024-01-05 [Neologisms] [Language]...
15. Strong perfect graph theorem: In graph theory, the strong perfect graph theorem is a forbidden graph characterization of the perfect graphs as being exactly the graphs that have neither odd holes (odd-length induced cycles of length at least 5) nor odd antiholes (complements ... (Perfect graphs have neither odd holes nor odd antiholes) [86%] 2023-07-11 [Perfect graphs] [Theorems in graph theory]...
16. Spectral graph theory: In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix. The adjacency matrix ... (Linear algebra aspects of graph theory) [80%] 2024-01-12 [Algebraic graph theory] [Spectral theory]...
17. Extremal graph theory: Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory. In essence, extremal graph theory studies how global properties of a graph influence local substructure. [80%] 2023-09-18 [Extremal graph theory]
18. Spectral Graph Theory: This page, as of now, contains resources to learn spectral graph theory. [80%] 2024-01-12 [Graph theory]
19. Geometric graph theory: Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter sense, geometric graph theory studies combinatorial and geometric properties of geometric graphs, meaning graphs ... (Subfield of graph theory) [80%] 2023-09-10 [Geometric graph theory]
20. Evolutionary graph theory: Evolutionary graph theory is an area of research lying at the intersection of graph theory, probability theory, and mathematical biology. Evolutionary graph theory is an approach to studying how topology affects evolution of a population. (Approach to studying how topology affects evolution of a population) [80%] 2024-01-12 [Evolution] [Application-specific graphs]...