Ebook: Thirty Essays on Geometric Graph Theory

In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of "abstract" graph theory are often incapable of providing satisfactory answers to questions arising in such applications. In the past couple of decades, many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoning field with many striking results and appealing open questions.

This contributed volume contains thirty original survey and research papers on important recent developments in geometric graph theory. The contributions were thoroughly reviewed and written by excellent researchers in this field.

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In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of "abstract" graph theory are often incapable of providing satisfactory answers to questions arising in such applications. In the past couple of decades, many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoning field with many striking results and appealing open questions.

This contributed volume contains thirty original survey and research papers on important recent developments in geometric graph theory. The contributions were thoroughly reviewed and written by excellent researchers in this field.

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In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of "abstract" graph theory are often incapable of providing satisfactory answers to questions arising in such applications. In the past couple of decades, many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoning field with many striking results and appealing open questions.

This contributed volume contains thirty original survey and research papers on important recent developments in geometric graph theory. The contributions were thoroughly reviewed and written by excellent researchers in this field.

Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-4
The Maximum Number of Tangencies Among Convex Regions with a Triangle-Free Intersection Graph....Pages 5-18
Blocking Colored Point Sets....Pages 19-30
Constrained Tri-Connected Planar Straight Line Graphs....Pages 31-48
Topological Hypergraphs....Pages 49-70
On Edge-Disjoint Empty Triangles of Point Sets....Pages 71-81
Universal Sets for Straight-Line Embeddings of Bicolored Graphs....Pages 83-100
Drawing Trees, Outerplanar Graphs, Series-Parallel Graphs, and Planar Graphs in a Small Area....Pages 101-119
The Crossing-Angle Resolution in Graph Drawing....Pages 121-165
Mover Problems....Pages 167-184
Rectangle and Square Representations of Planar Graphs....Pages 185-211
Convex Obstacle Numbers of Outerplanar Graphs and Bipartite Permutation Graphs....Pages 213-248
Hanani–Tutte, Monotone Drawings, and Level-Planarity....Pages 249-261
On Disjoint Crossing Families in Geometric Graphs....Pages 263-287
Counting Plane Graphs: Flippability and Its Applications....Pages 289-302
Plane Geometric Graph Augmentation: A Generic Perspective....Pages 303-325
Discrete Geometry on Red and Blue Points in the Plane Lattice....Pages 327-354
Ramsey-Type Problems for Geometric Graphs....Pages 355-369
Blockers for Noncrossing Spanning Trees in Complete Geometric Graphs....Pages 371-382
Counting Large Distances in Convex Polygons: A Computational Approach....Pages 383-397
Coloring Distance Graphs and Graphs of Diameters....Pages 399-414
Realizability of Graphs and Linkages....Pages 415-428
A Note on Geometric 3-Hypergraphs....Pages 429-460
Favorite Distances in High Dimensions....Pages 461-482
Intersection Patterns of Convex Sets via Simplicial Complexes: A Survey....Pages 483-487
Construction of Locally Plane Graphs with Many Edges....Pages 489-498
A Better Bound for the Pair-Crossing Number....Pages 499-519
Minors, Embeddability, and Extremal Problems for Hypergraphs....Pages 521-540
Erratum to....Pages 541-562
....Pages 563-567