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 …

A queue layout of a graph consists of a total order of the vertices, and a partition of the edges
into queues, such that no two edges in the same queue are nested. The minimum number of …

It has been long conjectured that the crossing number of Cm× Cn is (m− 2) n, for all m, n
such that n≥ m≥ 3. In this paper, it is shown that if n≥ m (m+ 1) and m≥ 3, then this …

Tree decompositions of graphs are of fundamental importance in structural and algorithmic
graph theory. Planar decompositions generalise tree decompositions by allowing an …

We describe a method of creating an infinite family of crossing‐critical graphs from a single
small planar map, the tile, by gluing together many copies of the tile together in a circular …

62] Turan, P., A note of welcome, J. Graph Theory 1 (1977) 7-9. 63] Dambitis, J., An
algorithm for superimposing a nonplanar graph onto the plane with nearly minimal number …

We show that if a very large grid is embedded in a surface, then a large subgrid is
embedded in a disc in the surface. This readily implies that:(a) a minor-minimal graph that …

Bhatt and Leighton proved that the crossing number of a network (graph) is closely related to
the minimum layout area required for the implementation of a VLSI circuit for that network …

It is very well-known that there are precisely two minimal non-planar graphs: K 5 and K 3, 3
(degree 2 vertices being irrelevant in this context). In the language of crossing numbers …