InfiniteGraph is a distributed graph database implemented in Java and C++ and is from a class of NOSQL ("Not Only SQL") database technologies that focus...
5 KB (473 words) - 00:05, 7 January 2024
Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...
106 KB (15,667 words) - 12:01, 16 May 2024
A graph database (GDB) is a database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data. A key...
51 KB (4,647 words) - 12:09, 25 July 2024
finite graphs either do not extend to the infinite case or need a rather different proof. An empty graph is a graph that has an empty set of vertices (and...
28 KB (3,689 words) - 00:52, 14 August 2024
Eulerian path (redirect from Eulerian graph)
In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices)...
27 KB (3,269 words) - 06:54, 4 May 2024
Ramsey's theorem (category Theorems in graph theory)
infinite form of Ramsey's theorem for graphs, the Erdős–Dushnik–Miller theorem, states that every infinite graph contains either a countably infinite...
62 KB (7,919 words) - 16:19, 31 July 2024
graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject...
67 KB (7,996 words) - 03:26, 15 August 2024
Trémaux tree (category Infinite graphs)
especially in the context of infinite graphs. All depth-first search trees and all Hamiltonian paths are Trémaux trees. In finite graphs, every Trémaux tree is...
17 KB (2,301 words) - 17:03, 8 February 2024
are not true (or are rather different) for infinite graphs because many of the arguments fail in the infinite case. Moreover, V {\displaystyle V} is often...
52 KB (6,403 words) - 06:09, 18 June 2024
Four color theorem (category Graph coloring)
finite planar graphs, but also to infinite graphs that can be drawn without crossings in the plane, and even more generally to infinite graphs (possibly with...
48 KB (6,174 words) - 05:29, 18 August 2024
a universal graph is an infinite graph that contains every finite (or at-most-countable) graph as an induced subgraph. A universal graph of this type...
8 KB (865 words) - 17:36, 25 September 2022
In the mathematics of infinite graphs, an end of a graph represents, intuitively, a direction in which the graph extends to infinity. Ends may be formalized...
21 KB (3,109 words) - 12:20, 25 November 2023
In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with...
38 KB (5,155 words) - 02:30, 23 March 2024
the infinite graph, as in "an 8 × 8 square grid". The term lattice graph has also been given in the literature to various other kinds of graphs with...
4 KB (526 words) - 12:30, 2 June 2023
Breadth-first search (category Graph algorithms)
the application of graph traversal methods in artificial intelligence the input may be an implicit representation of an infinite graph. In this context...
14 KB (1,846 words) - 10:22, 14 May 2024
Spanning tree (category Computational problems in graph theory)
of graph theory, a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G. In general, a graph may...
26 KB (3,265 words) - 23:16, 10 December 2023
K6-minor-free graph is an apex graph Does a Moore graph with girth 5 and degree 57 exist? Do there exist infinitely many strongly regular geodetic graphs, or any...
190 KB (19,544 words) - 11:00, 17 August 2024
In graph theory, the Henson graph Gi is an undirected infinite graph, the unique countable homogeneous graph that does not contain an i-vertex clique...
3 KB (414 words) - 17:23, 16 April 2020
extension of the concept of graph density defined above from finite graphs to infinite graphs. Intuitively, an infinite graph has arbitrarily large finite...
9 KB (1,166 words) - 06:11, 25 March 2024
mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each...
51 KB (6,580 words) - 02:26, 3 January 2024
Handshaking lemma (category Lemmas in graph theory)
In graph theory, a branch of mathematics, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch...
29 KB (3,574 words) - 06:35, 13 February 2023
Random walk (section On graphs)
can consider random walks on crystal lattices (infinite-fold abelian covering graphs over finite graphs). Actually it is possible to establish the central...
55 KB (7,633 words) - 12:22, 17 August 2024
In graph theory, a k-degenerate graph is an undirected graph in which every subgraph has a vertex of degree at most k: that is, some vertex in the subgraph...
29 KB (3,393 words) - 06:36, 11 January 2024
Dijkstra's algorithm (category Graph algorithms)
an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, road networks. It was conceived by computer...
46 KB (5,896 words) - 14:05, 7 July 2024
Kőnig's lemma (category Infinite graphs)
theorem in graph theory due to the Hungarian mathematician Dénes Kőnig who published it in 1927. It gives a sufficient condition for an infinite graph to have...
17 KB (2,294 words) - 22:05, 16 August 2024
Hadwiger–Nelson problem (category Infinite graphs)
question can be phrased in graph theoretic terms as follows. Let G be the unit distance graph of the plane: an infinite graph with all points of the plane...
16 KB (1,866 words) - 08:08, 6 May 2024
Menger's theorem (category Graph connectivity)
In the mathematical discipline of graph theory, Menger's theorem says that in a finite graph, the size of a minimum cut set is equal to the maximum number...
11 KB (1,598 words) - 04:43, 7 April 2024
Transitive reduction (category Graph theory)
and is a subgraph of the given graph. However, uniqueness fails for graphs with (directed) cycles, and for infinite graphs not even existence is guaranteed...
16 KB (2,273 words) - 13:23, 28 May 2024
Diamond cubic (category Infinite graphs)
involves the removal of some of the edges from a three-dimensional grid graph. In this coordinatization, which has a distorted geometry from the standard...
12 KB (1,491 words) - 16:31, 8 June 2024