Vol 20 No. 1

Topological complexity and related invariants
Yuli B. Rudyak
Early this century, Michael Farber introduced and developed the notion of topological complexity, applying it to robotics (in greater detail, to robot motion planning). This is a numerical invariant of Lusternik–Schnirelmann type. We survey recent progress in the area.
Autenticación mediante conocimiento nulo en base a ecuaciones cuadráticas
José Luis Juan Herrera, García Guillermo Morales Luna, Feliú Sagols Troncoso
Presentamos una alternativa a los métodos actuales de autenticación con conocimiento nulo, basada ésta en el método aceite-vinagre no-equilibrado (Unbalanced Oil and Vinegar ). Con esto, se tiene un método alterno a los actuales, basados en diversos problemas computacionalmente difíciles.
A bound on the size of irreducible triangulations
Gloria Aguilar Cruz, Francisco Javier Zaragoza Martínez
Let S be a closed surface with Euler genus γ(S). An irreducible triangulation of S is a simple graph G without contractible edges embedded on S so that each face is a triangle and any two faces share at most one edge. Nakamoto and Ota were the first to give a linear upper bound for the number n of vertices of G in terms of γ(S). This bound was recently improved for orientable surfaces. By extending Nakamoto and Ota’s method we improve on these bounds by showing that n ≤ 106.5γ(S)−33 for any closed surface S.