This paper puts forward a new notion of a proof based on computational complexity and explores its implications for computation at large. Computationally sound proofs provide, in a...
Abstract. We analyze results on well-partial-orderings from the viewpoint of computability theory, and we answer a question posed by Diana Schmidt. We obtain the following results....
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...