In graph theory, the De Bruijn–Erdős theorem relates graph coloring of an infinite graph to the same problem on its finite subgraphs. It states that,...

The De Bruijn–Erdős theorem may refer to: De Bruijn–Erdős theorem (incidence geometry) De Bruijn–Erdős theorem (graph theory) This disambiguation page...

proof of the theorem for finite planar graphs with the De Bruijn–Erdős theorem stating that, if every finite subgraph of an infinite graph is k-colorable...

computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context...

Courcelle's theorem (graph theory) De Bruijn–Erdős theorem (graph theory) Dirac's theorems (graph theory) Erdős–Gallai theorem (graph theory) Erdős–Ginzburg–Ziv...

symbols De Bruijn–Erdős theorem (disambiguation) De Bruijn–Erdős theorem (graph theory), a theorem about graph coloring De Bruijn–Erdős theorem (incidence...

the De Bruijn–Newman constant, the De Bruijn–Erdős theorem, in graph theory, a different theorem of the same name: the De Bruijn–Erdős theorem in incidence...

In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges...

Paul Erdős: de Bruijn–Erdős theorem (graph theory) de Bruijn–Erdős theorem (incidence geometry) Davenport–Erdős theorem Erdős–Anning theorem Erdős–Beck...

w-colorable incomparability graph. Therefore, by the De Bruijn–Erdős theorem, P itself also has a w-colorable incomparability graph, and thus has the desired...

assumption of the axiom of choice. This is the de Bruijn–Erdős theorem of de Bruijn & Erdős (1951). If a graph admits a full n-coloring for every n ≥ n0,...

graph Cage (graph theory) Cayley graph Circle graph Clique graph Cograph Common graph Complement of a graph Complete graph Cubic graph Cycle graph De...

compactness, such as the De Bruijn–Erdős theorem stating that every minimal k-chromatic graph is finite, and the Curtis–Hedlund–Lyndon theorem providing a topological...

distance graphs, and more specifically of the infinite unit distance graph formed from all points of the Euclidean plane. By the de Bruijn–Erdős theorem, which...

discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential...

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)...

problem Sylvester–Gallai theorem and De Bruijn–Erdős theorem Cauchy's theorem Borsuk's conjecture Schröder–Bernstein theorem Wetzel's problem on families...

only one component. G {\displaystyle G} is finite (this is the De Bruijn–Erdős theorem). The minimum degree δ ( G ) {\displaystyle \delta (G)} obeys the...

Franel and Edmund Landau in 1924. The de Bruijn–Newman constant denoted by Λ and named after Nicolaas Govert de Bruijn and Charles M. Newman, is defined as...

leave out "Hausdorff" we get a theorem equivalent to the full axiom of choice. In graph theory, the de Bruijn–Erdős theorem is another equivalent to BPI...

{\displaystyle n} different lines. This result is known as the De Bruijn–Erdős theorem. As a base case, the result is clearly true for n = 3 {\displaystyle...

most one unit. The De Bruijn–Erdős theorem may be used to transfer many edge coloring properties of finite graphs to infinite graphs. For instance, Shannon's...

prime factors. Erdős conjectures Fuglede's conjecture Millennium Prize Problems Painlevé conjecture Mathematical fallacy Superseded theories in science List...

Hesse configuration. A related result is the de Bruijn–Erdős theorem. Nicolaas Govert de Bruijn and Paul Erdős proved the result in the more general setting...

algebraic closure (for a countable field). The De Bruijn–Erdős theorem for countable graphs: every countable graph whose finite subgraphs are k {\displaystyle...

 310–316 Erdős, P.; Lovász, L.; Simmons, A.; Straus, E. G. (1973), "Dissection graphs of planar point sets", A Survey of Combinatorial Theory (Proc. Internat...

"finding the chromatic number of the plane". By the de Bruijn–Erdős theorem, a result of de Bruijn & Erdős (1951), the problem is equivalent (under the assumption...

biographical material on Paul Erdős, Frank P. Ramsey, Emmy Noether, Alfred Brauer, Richard Courant, Kenneth Falconer, Nicolas de Bruijn, Hillel Furstenberg, and...

Berlekamp switching game Salem–Spencer set Secretary problem Tournament (graph theory) Erdős distinct distances problem Leo Moser at the Mathematics Genealogy...

unit distance graph of the plane, the graph of the plane also requires at least four colors in any coloring. By the de Bruijn–Erdős theorem (with the assumption...