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 …

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 …

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 …

We show that every complete n-vertex simple topological graph contains a topological
subgraph on at least (log n) 1/4-o (1) vertices that is weakly isomorphic to the complete …

In 1988 Rafla conjectured that every simple drawing of a complete graph $ K_n $ contains a
plane, ie, non-crossing, Hamiltonian cycle. The conjecture is far from being resolved. The …

Simple drawings are drawings of graphs in the plane or on the sphere such that vertices are
distinct points, edges are Jordan arcs connecting their endpoints, and edges intersect at …

Borrowing László Székely's lively expression, we show that Hill's conjecture is
“asymptotically at least 98.5\% true.” This long-standing conjecture states that the crossing …

It is a longstanding conjecture that every simple drawing of a complete graph on $ n\geq 3$
vertices contains a crossing-free Hamiltonian cycle. We strengthen this conjecture to" there …

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 …

Topological drawings are representations of graphs in the plane, where vertices are
represented by points, and edges by simple curves connecting the points. A drawing is …