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 …

Crossing Numbers of Graphs is the first book devoted to the crossing number, an
increasingly popular object of study with surprising connections. The field has matured into a …

Abstract We study Hanani-Tutte style theorems for various notions of planarity, including
partially embedded planarity, and simultaneous planarity. This approach brings together the …

Simple drawings are drawings of graphs in which the edges are Jordan arcs and each pair
of edges share at most one point (a proper crossing or a common endpoint). A simple …

Given two planar graphs G_1 G 1 and G_2 G 2 that share some vertices and edges, a
simultaneous embedding with fixed edges (Sefe) is a pair of planar topological …

In 1958, Hill conjectured that the minimum number of crossings in a drawing of K_n K n is
exactly Z (n)= 1 4\big ⌊ n 2\big ⌋\big ⌊ n-1 2\big ⌋\big ⌊ n-2 2\big ⌋\big ⌊ n-3 2\big ⌋ Z (n) …

Abstract Let G=(V, E) be a directed graph and ℓ: V→[k]:={1,…, k} a level assignment such
that ℓ (u)< ℓ (v) for all directed edges (u, v)∊ E. A level planar drawing of G is a drawing of G …

The problem Level Planarity asks for a crossing-free drawing of a graph in the plane such
that vertices are placed at prescribed y-coordinates (called levels) and such that every edge …

Abstract The Harary–Hill Conjecture states that the number of crossings in any drawing of
the complete graph K_n K n in the plane is at least Z (n):= 1 4\left ⌊ n 2\right ⌋\left ⌊ n-1 …

The problem Level Planarity asks for a crossing-free drawing of a graph in the plane such
that vertices are placed at prescribed y-coordinates (called levels) and such that every edge …