Quasiplanar graphs, string graphs, and the Erdős-Gallai problem

Graph theory (including graph drawing) in computer science (68R10) Planar graphs; geometric and topological aspects of graph theory (05C10) Erd?s problems and related topics of discrete geometry (52C10) Graph representations (geometric and intersection representations, etc.) (05C62)

Cites Work

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Triangle-free intersection graphs of line segments with large chromatic number
Coloring $K_{k}$-free intersection graphs of geometric objects in the plane
On generalized Ramsey numbers of Erdős and Rogers
Coloring intersection graphs of $x$-monotone curves in the plane
On $K_s$-free subgraphs in $K_{s+k}$-free graphs and vertex Folkman numbers
On-line approach to off-line coloring problems on graphs with geometric representations
On the maximum number of edges in quasi-planar graphs
Separator theorems and Turán-type results for planar intersection graphs
On the maximum number of edges in topological graphs with no four pairwise crossing edges
On the chromatic number of multiple interval graphs and overlap graphs
Covering and coloring polygon-circle graphs
Quasi-planar graphs have a linear number of edges
On geometric graphs with no $k$ pairwise parallel edges
$K_4$-free graphs without large induced triangle-free subgraphs
Triangle-free geometric intersection graphs with no large independent sets
Coloring curves that cross a fixed curve
A Separator Theorem for String Graphs and its Applications
Research Problems in Discrete Geometry
On a Coloring Problem.
Generalized Nested Dissection
K^s-Free Graphs Without Large K^r-Free Subgraphs
Separators in region intersection graphs
Large K_r‐free subgraphs in K_s‐free graphs and some other Ramsey‐type problems
Bounding Ramsey numbers through large deviation inequalities
Quasi-planar Graphs
Circle graphs are quadratically χ‐bounded
Improved bounds for colouring circle graphs
Improved bounds for the Erdős-Rogers function
Outerstring Graphs are $\chi$-Bounded
Applications of a New Separator Theorem for String Graphs
The Construction of Certain Graphs
String graphs and incomparability graphs
Colouring arcwise connected sets in the plane. I
Coloring and Maximum Weight Independent Set of Rectangles
String graphs have the Erdős-Hajnal property

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