The crossing number is a popular tool in graph drawing and visualization, but there is not
really just one crossing number; there is a large family of crossing number notions of which …

We present, to the best of the authors' knowledge, all known results for the (planar) crossing
numbers of specific graphs and graph families. The results are separated into various …

Let h (n) be the minimum integer such that every complete n-vertex simple topological graph
contains an edge that crosses at most h (n) other edges. In 2009, Kynčl and Valtr showed …

Turán's famous tetrahedron problem is to compute the Turán density of the tetrahedron K 4 3
K_4^3. This is equivalent to determining the maximum ℓ 1 ℓ_1‐norm of the codegree vector …

The long standing Zarankiewicz's conjecture states that the crossing number cr (K m, n) of
the complete bipartite graph is Z (m, n):=[m/2][m-1/2][n/2][n-1/2]. Using flag algebras we …

We apply ideas from the theory of limits of dense combinatorial structures to study order
types, which are combinatorial encodings of finite point sets. Using flag algebras we obtain …

In this work, we introduce and develop a theory of convex drawings of the complete graph $
K_n $ in the sphere. A drawing $ D $ of $ K_n $ is convex if, for every 3-cycle $ T $ of $ K_n …

In this paper, we use semidefinite programming and representation theory to compute new
lower bounds on the crossing number of the complete bipartite graph K m, n, extending a …

In this paper, we use semidefinite programming and representation theory to compute new
lower bounds on the crossing number of the complete bipartite graph $ K_ {m, n} …

Let $ x_1,..., x_n $ be a list of real numbers, let $ s:=\sum_ {i= 1}^{n} x_i $, and let $
h:\mathbb {N}\rightarrow\mathbb {R} $ be a function. We gave a necessary and sufficient …