Titlebook: Computational Discrete Mathematics; Advanced Lectures Helmut Alt Textbook 2001 Springer-Verlag Berlin Heidelberg 2001 Computer.Discrete mat

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https://doi.org/10.1007/978-3-658-38187-5in high dimensions (in particular for . ≥ 561, due to Kahn & Kalai, Nilli, and Raigorodskii), and yields the known counter-examples to Borsuk’s problem posed in 1933..Here we ask whether there might be counterexamples in low dimension as well. We show that there is no counterexample to the 0/1-Borsu

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Codes over ,, ,inary nonlinear codes better than comparable binary linear codes. This connection between linear codes over . . and nonlinear binary codes was also the breakthrough in solving an old puzzle of the apparent duality between the nonlinear Kerdock and Preparata codes. We present a description of this puzzle and a brief introduction to codes over . ..

AMBI

Degree Bounds for Long Paths and Cycles in ,-Connected Graphs,the vertex set .. To see this, consider a longest .-path . and a longest .- path . in . For the first vertex . on . in . we then have . and ., consequently .. Here . and |G| denote the number of vertices on . and in . respectively.

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Apoptosis

https://doi.org/10.1007/3-540-45506-XComputer; Discrete mathematics; Mapping; algorithms; coding; coding theory; combinatorics; computational al

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978-3-540-42775-9Springer-Verlag Berlin Heidelberg 2001

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Outshine

Explicit and Implicit Enforcing - Randomized Optimization,veral linear time methods are available, and some of them even behave ‘well’ when the dimension grows; at least, no better provable behavior is known. Many of the methods can be interpreted as variants of the simplex algorithm, with appropriately chosen randomized pivot rules.