Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory...

Bollobás's first publication was a joint publication with Erdős on extremal problems in graph theory, written when he was in high school in 1962. With Erdős's...

areas of spectral graph theory, extremal graph theory and random graphs, in particular in generalizing the Erdős–Rényi model for graphs with general degree...

spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are...

many edges. Thus it has its application in extremal graph theory, additive combinatorics and Ramsey theory. Let u , n , r , m , t ∈ N {\displaystyle u...

the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or n-fan) Fn is a planar, undirected graph with 2n + 1 vertices and...

number of edges in a graph that does not have a fixed Turán graph as a subgraph. Via this theorem, similar bounds in extremal graph theory can be proven for...

extremal graph theory, the Erdős–Stone theorem is an asymptotic result generalising Turán's theorem to bound the number of edges in an H-free graph for...

Ramsey-Turán theory is a subfield of extremal graph theory. It studies common generalizations of Ramsey's theorem and Turán's theorem. In brief, Ramsey-Turán...

algorithm Graph theorists Algebraic graph theory Geometric graph theory Extremal graph theory Probabilistic graph theory Topological graph theory Graph drawing...

size. It is one of the central results of extremal graph theory, an area studying the largest or smallest graphs with given properties, and is a special...

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...

Extremal combinatorics is a field of combinatorics, which is itself a part of mathematics. Extremal combinatorics studies how large or how small a collection...

In extremal graph theory, the even circuit theorem is a result of Paul Erdős according to which an n-vertex graph that does not have a simple cycle of...

MR 0360330 Erdős, P.; Simonovits, M. (1973), "On a valence problem in extremal graph theory", Discrete Mathematics, 5 (4): 323–334, doi:10.1016/0012-365X(73)90126-X...

Sárközy, and Endre Szemerédi in 1997, is an important result in extremal graph theory, particularly within the context of the regularity method. It states...

area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently...

In graph theory, the metric dimension of a graph G is the minimum cardinality of a subset S of vertices such that all other vertices are uniquely determined...

(1978), Extremal Graph Theory, LMS Monographs, vol. 11, Academic Press, MR 0506522. Fowler, Thomas (1998), Unique Coloring of Planar Graphs (PDF), Ph...

theorem. Ergodic Ramsey theory Extremal graph theory Goodstein's theorem Bartel Leendert van der Waerden Discrepancy theory Graham, Ron; Butler, Steve...

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...

extremal graph theory. Turán's best-known result in this area is Turán's graph theorem, that gives an upper bound on the number of edges in a graph that...

In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first...

Distribution theory Dynamical systems theory Elimination theory Ergodic theory Extremal graph theory Field theory Galois theory Game theory Graph theory Group...

In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique...

In graph theory, a clique (/ˈkliːk/ or /ˈklɪk/) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are...

Euler tours; extremal graph theory; subgraph counting problems including connections to permutations, derangements, and Cayley's formula; graph labelings;...

Hungarian-style combinatorics, particularly Ramsey theory, extremal graph theory, combinatorial number theory, and probabilistic methods in combinatorics. He...

graph theory, which focuses on embeddings of graphs in surfaces (that is, drawings without crossings). A fundamental problem in extremal graph theory...

In graph theory, an area of mathematics, common graphs belong to a branch of extremal graph theory concerning inequalities in homomorphism densities....