Thirty Essays on Geometric Graph Theory 1st ed. 2013, Corr. 2nd printing 2013 edition

Marc Notes: The field of geometric graph theory is a fairly new discipline. This contributed volume contains 30 original survey and research papers on important recent developments in geometric graph theory written by active researchers in this field. Table of Contents: Introduction.- 1) B. Abrego - S. Fernandez-Merchant - G. Salazar: The rectilinear crossing number of K_n: closing in (or are we?).- 2) E. Ackerman: The maximum number of tangencies among convex regions with a triangle-free intersection graph.- 3) G. Aloupis - B. Ballinger - S. Collette - S. Langerman - A. Por - D. R. Wood: Blocking coloured point sets.- 4) M. Al-Jubeh - G. Barequet - M. Ishaque - D. Souvaine - Cs. D. Toth - A. Winslow: Constrained tri-connected planar straight line graphs.- 5) S. Buzaglo - R. Pinchasi - G. Rote: Topological hypergraphs.- 6) J. Cano Vila - L. F. Barba - J. Urrutia - T. Sakai: On edge-disjoint empty triangles of point sets.- 7) J. Cibulka - J. Kyn l - V. Meszaros - R. Stola - P. Valtr: Universal sets for straight-line embeddings of bicolored graphs.- 8) G. Di Battista - F. Frati: Drawing trees, outerplanar graphs, series-parallel graphs, and planar graphs in small area.- 9) W. Didimo - G. Liotta: The crossing angle resolution in graph drawing.- 10) A. Dumitrescu: Mover problems.- 11) S. Felsner: Rectangle and square representations of planar graphs.- 12) R. Fulek - N. Saeedi - D. Sarioz: Convex obstacle numbers of outerplanar graphs and bipartite permutation graphs.- 13) R. Fulek - M. Pelsmajer - M. Schaefer - D. tefankovi: Hanani-Tutte, monotone drawings, and level-planarity.- 14) R. Fulek - A. Suk: On disjoint crossing families in geometric graphs.- 15) M. Hoffmann - A. Schulz - M. Sharir - A. Sheffer - Cs. D. Toth - E. Welzl: Counting plane graphs: flippability and its applications.- 16) F. Hurtado - Cs. D. Toth: Geometric graph augmentation: a generic perspective.- 17) M. Kano - K. Suzuki: Discrete geometry on red and blue points in the plane lattice.- 18) Gy. Karolyi: Ramsey-type problems for geometric graphs.- 19) Ch. Keller - M. Perles - E. Rivera-Campo - V. Urrutia-Galicia: Blockers for non-crossing spanning trees in complete geometric graphs.- 20) A. V. Kostochka - K. G. Milans: Coloring clean and K_4-free circle graphs.- 21) F. Mori - D. Pritchard: Counting large distances in convex polygons: a computational approach.- 22) A. Raigorodskii: Coloring distance graphs and graphs of diameters.- 23) M. Schaefer: Realizability of graphs and linkages.- 24) C. Smyth: Equilateral sets in l_dp.- 25) A. Suk: A note on geometric 3-hypergraphs.- 26) K. Swanepoel: Favourite distances in high dimensions.- 27) M. Tancer: Intersection patterns of convex sets via simplicial complexes, a survey.- 28) G. Tardos: Construction of locally plane graphs with many edges.- 29) G. Toth: A better bound for the pair-crossing number.- 30) U. Wagner: Minors, embeddability, and extremal problems for hypergraphs."Biographical Note: Janos Pach is a mathematician and computer scientist with academic and research positions in the following institutions: Ecole Polytechnique Federale de Lausanne, Alfred Renyi Institute of Mathematics at Hungarian Academy of Sciences, and Courant Institute of Mathematics at NYU."Jacket Description/Back: 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."

Contributor Bio:  Pach, Janos About the authors JANOS PACH is Professor of Computer Science at City College of New York and Senior Research Fellow at the Mathematical Institute of the Hungarian Academy of Sciences. He received his PhD in mathematics from Eotvos University, Budapest, in 1980 and has had visiting positions at various universities, including the University College of London, McGill University, the Courant Institute of New York University, and Tel Aviv University. He serves on the editorial boards of three mathematical and computer science journals and has been an invited speaker at many conferences. He has published more than one hundred research papers, mostly in discrete and computational geometry and in combinatorics. He received the Lester R. Ford Award in 1990 and the Renyi Prize in 1993. PANKAJ K. AGARWAL is Associate Professor in the Computer Science Department of Duke University. He received his PhD in computer science from the Courant Institute of Mathematical Sciences, New York University, in 1989. He is the author of Intersection and Decomposition Algorithms for Planar Arrangements, and a coauthor of Davenport--Schinzel Sequences and Their Geometric Applications. He has published several research papers and has given talks at many conferences. He was awarded the National Young Investigator Award in 1992.