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 …

Given a finite, undirected, simple graph G, we are concerned with operations on G that
transform it into a planar graph. We give a survey of results about such operations and …

This textbook covers a diversity of topics in graph and network theory, both from a theoretical
standpoint, and from an applied modelling point of view. Mathematica® is used to …

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

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 …

The Excluded Minors for Embeddability into a Compact Surface | Combinatorica Skip to
main content Springer Nature Link Account Menu Find a journal Publish with us Track your …

The k-planar crossing number of a graph is the minimum number of crossings of its edges
over all possible drawings of the graph in k planes. We propose algorithms and methods for …

The crossing number of a graph $ G $ is the minimum number of crossings in a drawing of $
G $ in the plane. A rectilinear drawing of a graph $ G $ represents vertices of $ G $ by a set …

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 …

A graph is k-planar, if it admits a drawing with at most k crossings per edge. Testing whether
a given graph is k-planar is known to be NP-complete. For k= 1 the problem remains NP …