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On homotopy types of limits of semi-algebraic sets and additive complexity of polynomials

Sal Barone, Saugata Basu (2014)

Journal of the European Mathematical Society

We prove that the number of distinct homotopy types of limits of one-parameter semi-algebraic families of closed and bounded semi-algebraic sets is bounded singly exponentially in the additive complexity of any quantifier-free first order formula defining the family. As an important consequence, we derive that the number of distinct homotopy types of semi-algebraic subsets of ℝ k defined by a quantifier-free first order formula Φ , where the sum of the additive complexities of the polynomials appearing...

On k -pairable graphs from trees

Zhongyuan Che (2007)

Czechoslovak Mathematical Journal

The concept of the k -pairable graphs was introduced by Zhibo Chen (On k -pairable graphs, Discrete Mathematics 287 (2004), 11–15) as an extension of hypercubes and graphs with an antipodal isomorphism. In the same paper, Chen also introduced a new graph parameter p ( G ) , called the pair length of a graph G , as the maximum k such that G is k -pairable and p ( G ) = 0 if G is not k -pairable for any positive integer k . In this paper, we answer the two open questions raised by Chen in the case that the graphs involved...

On location problems on fuzzy graphs.

José A. Moreno Pérez, J. Marcos Moreno-Vega, José Luis Verdegay (2001)

Mathware and Soft Computing

Location problems concern a wide set of fields where it is usually assumed that exact data are known. However, in real applications, the location of the facility considered can be full of linguistic vagueness, that can be appropriately modeled using networks with fuzzy values. In that way arise Fuzzy Location Problems; this paper deals with their general formulation and the description solution methods. Namely we show the variety of problems that can be considered in this context and, for some of...

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