Thirty Essays on Geometric Graph Theory (eBook)

János Pach is a mathematician and computer scientist with academic and research positions in the following institutions: École Polytechnique Fédérale de Lausanne,  Alfréd Rényi Institute of Mathematics at Hungarian Academy of Sciences, and Courant Institute of Mathematics at NYU.

Introduction.- 1) B. Ábrego - S. Fernández-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. Pór - D.R.Wood: Blocking coloured point sets.- 4) M. Al-Jubeh - G. Barequet - M. Ishaque - D. Souvaine - Cs. D. Tóth - 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. Kynčl - V. Mészáros - R. Stolař - 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. Sariöz: Convex obstacle numbers of outerplanar graphs and bipartite permutation graphs.- 13) R. Fulek - M. Pelsmajer - M. Schaefer - D. Štefankovič: 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. Tóth - E. Welzl: Counting plane graphs: flippability and its applications.- 16) F. Hurtado - Cs. D. Tóth: Geometric graph augmentation: a generic perspective.- 17) M. Kano - K. Suzuki: Discrete geometry on red and blue points in the plane lattice.- 18) Gy. Károlyi: 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. Morić - 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. Tóth: A better bound for the pair-crossing number.- 30) U. Wagner: Minors, embeddability, and extremal problems for hypergraphs.