The graph crossing number and its variants: A survey

M Schaefer - The electronic journal of combinatorics, 2012 - combinatorics.org
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 …

[图书][B] Crossing numbers of graphs

M Schaefer - 2018 - taylorfrancis.com
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 …

Treewidth, circle graphs, and circular drawings

R Hickingbotham, F Illingworth, B Mohar… - SIAM Journal on Discrete …, 2024 - SIAM
A circle graph is an intersection graph of a set of chords of a circle. We describe the
unavoidable induced subgraphs of circle graphs with large treewidth. This includes …

Planar decompositions and the crossing number of graphs with an excluded minor

DR Wood, JA Telle - Graph Drawing: 14th International Symposium, GD …, 2007 - Springer
Tree decompositions of graphs are of fundamental importance in structural and algorithmic
graph theory. Planar decompositions generalise tree decompositions by allowing an …

[PDF][PDF] Crossing numbers of graphs: A bibliography

I Vrt'o - Available electronically at ftp://ifi. savba. sk/pub/imrich …, 2008 - Citeseer
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 …

[HTML][HTML] On the crossing numbers of loop networks and generalized Petersen graphs

G Salazar - Discrete mathematics, 2005 - Elsevier
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 …

An annotated glossary of graph theory parameters, with conjectures

R Gera, TW Haynes, ST Hedetniemi… - Graph Theory: Favorite …, 2018 - Springer
This glossary contains an annotated listing of some 300 parameters of graphs, together with
their definitions, and, for most of these, a reference to the authors who introduced them. Let …

[HTML][HTML] On k-planar crossing numbers

F Shahrokhi, O Sýkora, LA Székely, I Vrt'o - Discrete applied mathematics, 2007 - Elsevier
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 …

On Book Crossing Numbers of the Complete Graph

B Abrego, J Kinzel, S Fernandez-Merchant… - SIAM Journal on Discrete …, 2024 - SIAM
A-page book drawing of a graph is a drawing of on halfplanes with a line as a common
boundary such that the vertices are located on and the edges cannot cross. The-page book …

Various heuristic algorithms to minimise the two-page crossing numbers of graphs

H He, A Sălăgean, E Mäkinen, I Vrt'o - Open Computer Science, 2015 - degruyter.com
We propose several new heuristics for the twopage book crossing problem, which are based
on recent algorithms for the corresponding one-page problem. Especially, the neural …