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Titlebook: Geometry - Intuitive, Discrete, and Convex; A Tribute to László Imre Bárány,Károly J. Böröczky,János Pach Book 2013 Springer-Verlag Berlin

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Geometric Transversal Theory: ,(3)-Families in the Plane,A line that intersects every member of a finite family . of convex sets in the plane is called a line transversal to .. In this paper we will survey the main results and open problems concerning .(3)-families: Finite families of convex sets in the plane in which every subfamily of size 3 admit a line transversal.
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Hanani-Tutte and Related Results,We investigate under what conditions crossings of adjacent edges and pairs of edges crossing an even number of times are unnecessary when drawing graphs. This leads us to explore the Hanani-Tutte theorem and its close relatives, emphasizing the intuitive geometric content of these results.
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,Tarski’s Plank Problem Revisited,question and its variants continue to generate interest in the geometric and analytic aspects of coverings by planks in the present time as well. The paper is of a survey type with some new results and with a list of open research problems on the discrete geometric side of the plank problem.
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