A note on numerable covers

A Note on Range-Restricted Circuit Covers

A note on the size of minimal covers

For the class of monotone boolean functions f : {0,1}n → {0,1} where all 1-certificates have size 2, we prove the tight bound n (λ+ 2)2/4, where λ is the size of the largest 0-certificate of f . This result can be translated to graph language as follows: for every graph G= (V ,E) the inequality |V | (λ+ 2)2/4 holds, where λ is the size of the largest minimal vertex cover of G. In addition, ther...

A Note on Minimal Covers for Sofic Systems1

We characterize the sofic systems which have minimal subshift-of-fimtetype covers and derive some consequences. 0. Introduction. For relevant background, see §1. By a factor map, we mean a continuous onto shift commuting map between two symbolic systems. By definition, a sofic system S is a symbolic system which is a factor of a shift of finite type (SFT). In the language of automata theory, so...

A note about shortest cycle covers

Let G be a graph with odd edge-connectivity r. It is proved in this paper that if r > 3, then G has a 3-cycle (1, 2)-cover of total length at most ((r + 1)|E(G)|)/r . © 2005 Elsevier B.V. All rights reserved.

Note on dense covers in the category of locales

In this note we are going to study dense covers in the category of locales. We shall show that any product of finitely regular locales with some dense covering property has this property as well.