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RAC drawings of the complete graph K 5 and the complete bipartite graph K 3,4. In graph drawing, a RAC drawing of a graph is a drawing in which the vertices are represented as points, the edges are represented as straight line segments or polylines, at most two edges cross at any point, and when two edges cross they do so at right angles to each other.
The slope number of a graph is the minimum number of distinct edge slopes needed in a drawing with straight line segment edges (allowing crossings). Cubic graphs have slope number at most four, but graphs of degree five may have unbounded slope number; it remains open whether the slope number of degree-4 graphs is bounded.
The no-three-in-line drawing of a complete graph is a special case of this result with =. [12] The no-three-in-line problem also has applications to another problem in discrete geometry, the Heilbronn triangle problem. In this problem, one must place points, anywhere in a unit square, not restricted to a grid. The goal of the placement is to ...
Biju Patnaik University of Technology (BPUT) is a public state university located in Rourkela, Odisha, India. It was established on 21 November 2002 and named after Biju Patnaik , a former Chief Minister of Odisha .
The number of vertices is smaller when some lines are parallel, or when some vertices are crossed by more than two lines. [4] An arrangement can be rotated, if necessary, to avoid axis-parallel lines. After this step, each ray that forms an edge of the arrangement extends either upward or downward from its endpoint; it cannot be horizontal.
Lecture Notes in Mathematics is a book series in the field of mathematics, including articles related to both research and teaching. It was established in 1964 and was edited by A. Dold, Heidelberg and B. Eckmann, Zürich. Its publisher is Springer Science+Business Media (formerly Springer-Verlag).
Biju Patnaik University of Technology, also known as BPUT, is located in Rourkela in the state of Odisha, India. There are 110 colleges affiliated to the university. A college may be either a constituent or affiliated type. [1] The colleges are further classified as government run, private unaided and public private partnership (PPP) or private ...
Lecture Notes may refer to the following book series, published by Springer Science+Business Media Lecture Notes in Computer Science; Lecture Notes in Mathematics;