An annotated bibliography on 1-planarity

SG Kobourov, G Liotta, F Montecchiani - Computer Science Review, 2017 - Elsevier
The notion of 1-planarity is among the most natural and most studied generalizations of
graph planarity. A graph is 1-planar if it has an embedding where each edge is crossed by at …

[HTML][HTML] Colorings of plane graphs: a survey

OV Borodin - Discrete Mathematics, 2013 - Elsevier
After a brief historical account, a few simple structural theorems about plane graphs useful
for coloring are stated, and two simple applications of discharging are given. Afterwards, the …

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 …

Minimal obstructions for 1‐immersions and hardness of 1‐planarity testing

VP Korzhik, B Mohar - Journal of Graph Theory, 2013 - Wiley Online Library
A graph is 1‐planar if it can be drawn on the plane so that each edge is crossed by no more
than one other edge (and any pair of crossing edges cross only once). A non‐1‐planar …

[HTML][HTML] An introduction to the discharging method via graph coloring

DW Cranston, DB West - Discrete Mathematics, 2017 - Elsevier
We provide a “how-to” guide to the use and application of the Discharging Method. Our aim
is not to exhaustively survey results proved by this technique, but rather to demystify the …

[PDF][PDF] Topological graph theory

D Archdeacon - A survey. Congressus Numerantium, 1996 - math.u-szeged.hu
Graphs can be represented in many di erent ways: by lists of edges, by incidence relations,
by adjacency matrices, and by other similar structures. These representations are well suited …

A note on odd colorings of 1-planar graphs

DW Cranston, M Lafferty, ZX Song - Discrete Applied Mathematics, 2023 - Elsevier
A proper coloring of a graph is odd if every non-isolated vertex has some color that appears
an odd number of times on its neighborhood. This notion was recently introduced by …

Map graphs

ZZ Chen, M Grigni, CH Papadimitriou - Journal of the ACM (JACM), 2002 - dl.acm.org
We consider a modified notion of planarity, in which two nations of a map are considered
adjacent when they share any point of their boundaries (not necessarily an edge, as …

On the density of maximal 1-planar graphs

FJ Brandenburg, D Eppstein, A Gleißner… - … Symposium on Graph …, 2012 - Springer
A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most
once. It is maximal 1-planar if the addition of any edge violates 1-planarity. Maximal 1-planar …