For every k and r, we construct a finite family of axis-parallel rectangles in the plane such that no matter how we color them with k colors, there exists a point covered by prec...
We show that every plane graph with maximum face size four whose all faces of size four are vertex-disjoint is cyclically 5-colorable. This answers a question of Albertson whether...
In a recent paper, Brlek, Jamet and Paquin showed that some extremal infinite smooth words are also infinite Lyndon words. This result raises a natural question: are they the only...
We show that there exists a family of r-regular graphs of arbitrarily large excessive index for each integer r greater than 3. Furthermore, we answer a question in [1] showing tha...
We prove that there exists a weakly closed and bounded subset E of c0 which is not remotal from 0, and such that co (E) is remotal from 0. This answers a question of M. Mart´ın ...