# Category: Infinite graphs

Coordination sequence
In crystallography and the theory of infinite vertex-transitive graphs, the coordination sequence of a vertex is an integer sequence that counts how many vertices are at each possible distance from .
Universal graph
In mathematics, 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 was first constructed by Richard R
Diamond cubic
The diamond cubic crystal structure is a repeating pattern of 8 atoms that certain materials may adopt as they solidify. While the first known example was diamond, other elements in group 14 also adop
In geometric graph theory, the Hadwiger–Nelson problem, named after Hugo Hadwiger and Edward Nelson, asks for the minimum number of colors required to color the plane such that no two points at distan
Kőnig's lemma
Kőnig's lemma or Kőnig's infinity lemma is a 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 h
Henson graph
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 but that does contain all Ki-free finite graphs as
De Bruijn–Erdős theorem (graph theory)
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, when all finite subgraphs can be colored with colo
Halin's grid theorem
In graph theory, a branch of mathematics, Halin's grid theorem states that the infinite graphs with thick ends are exactly the graphs containing subdivisions of the hexagonal tiling of the plane. It w
Laves graph
In geometry and crystallography, the Laves graph is an infinite and highly symmetric system of points and line segments in three-dimensional Euclidean space, forming a periodic graph. Three equal-leng
Trémaux tree
In graph theory, a Trémaux tree of an undirected graph is a type of spanning tree, generalizing depth-first search trees.They are defined by the property that every edge of connects an ancestor–descen
Unfriendly partition
In the mathematics of infinite graphs, an unfriendly partition or majority coloring is a partition of the vertices of the graph into disjoint subsets, so that every vertex has at least as many neighbo
Young–Fibonacci lattice
In mathematics, the Young–Fibonacci graph and Young–Fibonacci lattice, named after Alfred Young and Leonardo Fibonacci, are two closely related structures involving sequences of the digits 1 and 2. An
End (graph theory)
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 mathematically as equivalence classes of in